This is a multi-part message in MIME format. ---------------0309050237747 Content-Type: text/plain; name="03-404.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-404.keywords" quantum mechanics, distributions, spectral theorem, Gel'fand triplets ---------------0309050237747 Content-Type: application/postscript; name="damp2.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="damp2.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: damp2.dvi %%CreationDate: Fri Sep 05 08:57:37 2003 %%Pages: 14 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: DVIPS.EXE damp2 %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.09.05:0857 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: special.pro %! TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N /vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N /rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N /@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ /hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B /@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ /urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known {userdict/md get type/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{ Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale }if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState save N userdict maxlength dict begin/magscale true def normalscale currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts /psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{ psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N/@beginspecial{SDict begin/SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{ CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR }{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end} repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N /@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X /yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet TeXDict begin 39158280 55380996 1000 600 600 (damp2.dvi) @start %DVIPSBitmapFont: Fa cmr5 5 3 /Fa 3 53 df<1360EA01E0120F12FF12F11201B3A3387FFF80A2111C7B9B1C>49 DI52 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb msbm9 9 1 /Fb 1 68 df67 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc cmsy9 9 3 /Fc 3 51 df<007FB712FCB812FEA26C16FC2F047A943C>0 D<013F16402601FFE015E0 4813F8487F4813FF4880D83FC06D1301273E001FE014C048D907F8130300786D6C130700 70D900FFEB0F8000F091387FE07F486EB512006F5B03075B6F5B03005B0040ED1F803312 7C9B3C>24 D<91383FFFF849B512FC1307011F14F8D93FE0C7FC01FFC8FCEA01FCEA03F0 485A485A5B48C9FC5A123E5AA21278A212F8A25AB712F816FCA216F800F0C9FC7EA21278 A2127CA27E123F7E6C7E7F6C7E6C7EEA01FC6CB4FCEB3FE06DB512F8010714FC1301D900 3F13F8262E7AA933>50 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd cmex9 9 4 /Fd 4 113 df<163C167C16F8ED01F0ED03E0ED07C0ED0F80ED1F00153E157E5D4A5A5D 14034A5A4A5A5D141F4AC7FCA2147E5CA2495AA2495AA2495AA2495AA2495AA2133F91C8 FC5B137EA213FE5BA212015BA21203A25B1207A25BA2120FA35B121FA45B123FA590C9FC 5AA912FEB3AA127FA97E7FA5121F7FA4120F7FA31207A27FA212037FA21201A27F1200A2 7F137EA2137F7F80131FA26D7EA26D7EA26D7EA26D7EA26D7EA2147E80A26E7E140F816E 7E6E7E1401816E7E157E153E81ED0F80ED07C0ED03E0ED01F0ED00F8167C163C26B27082 39>18 D<12F07E127C7E7E6C7E6C7E6C7E6C7E7F6C7E137E133E133F6D7E6D7E1307806D 7EA26D7E6D7EA2147EA280A26E7EA26E7EA26E7EA2811403811401A2811400A281157EA2 157FA2811680A2151FA216C0A3150F16E0A4150716F0A5150316F8A9ED01FCB3AAED03F8 A916F01507A516E0150FA416C0151FA31680A2153FA216005DA2157EA215FE5DA214015D A214035D14075DA24A5AA24A5AA24AC7FCA2147EA25CA2495A495AA2495A5C130F495A49 C8FC133E137E5B485A5B485A485A485A48C9FC123E5A5A5A26B27E8239>I101 D<1A0C1A1E1A3EA21A7CA21AF8A2F101F0A2 F103E0A2F107C0A2F10F80A2F11F00A2193EA261A261A24E5AA24E5AA24E5AA24E5AA24E C7FCA2183EA260A260A24D5AA24D5AA24D5AA201305E0170150F13F800034CC8FC487E00 0F163EEA3CFE00705E12E0D8407F5D12006D6C495AA26D6C495AA24C5A6D7E4C5A6D7E4C C9FC6D7E163EA26D6C5BA26D6C5BA291387F01F0A24B5AEC3F83ED87C0EC1FC7EDCF80EC 0FEF03FFCAFCA26E5AA26E5AA25D14015D6E5A475B78834D>112 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe lasy10 10.95 1 /Fe 1 51 df<007FB812E0B912F0A300F0CAFCB3B3A8B9FCA36C17E0343478B844>50 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff cmti10 10.95 50 /Ff 50 124 df39 D44 D<120FEA3FC0127FA212FFA3 1380EA7F00123C0A0A77891C>46 D<15031507150F151F151E153E157EEC01FEEC03FC14 07141FEB01FF90380FFBF8EB1FC3EB0E07130015F0A2140FA215E0A2141FA215C0A2143F A21580A2147FA21500A25CA25CA21301A25CA21303A25CA21307A25CA2130FA25CA2131F A25CEB7FE0B612F0A215E0203D77BC2E>49 D<15FE913803FFC091380F01F091383C00F8 4A137C4A7F4948133F49487F4A148049C7FC5BEB0E0C011E15C0EB1C0EEB3C0613381378 1370020E133FD9F00C148013E0141C0218137F00011600EBC0384A13FEEC600102E05B3A 00E3C003F89039FF0007F0013C495A90C7485A5E037FC7FC15FC4A5A4A5AEC0FC04AC8FC 147E14F8EB03E0495A011FC9FC133E49141801F0143C48481438485A1678485A48C85A12 0E001E4A5AD83FE0130301FF495A397C3FF01FD8780FB55AD8700391C7FCD8F0015B486C 6C5A6E5AEC07C02A3F79BC2E>II<131EEB3F80137FEBFFC05AA214806C13005B133C90C7FC B3120FEA3FC0127FA212FFA35B6CC7FC123C122777A61C>58 D<9339FF8001C0030F13E0 033F9038F803809239FF807E07913A03FC001F0FDA0FF0EB071FDA1FC0ECBF00DA7F806D B4FC4AC77E495AD903F86E5A495A130F4948157E4948157C495A13FF91C9FC4848167812 035B1207491670120FA2485A95C7FC485AA3127F5BA312FF5BA490CCFCA2170FA2170EA2 171E171C173C173817786C16706D15F04C5A003F5E6D1403001F4B5A6D4AC8FC000F151E 6C6C5C6C6C14F86C6C495A6C6CEB07C090397FC03F8090261FFFFEC9FC010713F0010013 803A4272BF41>67 D<49B712C018F818FE903B0003FE0003FF9438007F804BEC1FC0F00F E0F007F014074BEC03F8F001FCA2140F4BEC00FEA3141F4B15FFA3143F5DA3027F5D5DA2 19FE14FF92C81203A34917FC4A1507A219F813034A150F19F0A20107EE1FE05CF03FC0A2 010FEE7F804A16006060011F4B5A4A4A5A4D5AA2013F4B5A4AEC3FC04DC7FC017F15FEEE 03FC4AEB0FF001FFEC7FE0B8128004FCC8FC16E0403E7BBD45>I<49B812F8A390260003 FEC7121F18074B14031801F000F014075DA3140F5D19E0A2141F4B1338A2EF7801023F02 7013C04B91C7FCA217F0027F5CED80011603160F91B65AA3ED001F49EC07805CA3010392 C8FC5CF003804C13070107020E14005C93C75A180E010F161E4A151C183CA2011F5E5C60 A2013F15014A4A5A1707017F150F4D5A4A147F01FF913807FF80B9FCA295C7FC3D3E7BBD 3E>I<49B812F0A390260003FEC7123F180F4B1403A2F001E014075DA3140F5D19C0A214 1F5D1770EFF003023F02E013804B91C7FCA21601027F5CED8003A2160702FFEB1F8092B5 FCA349D9003FC8FC4A7F82A20103140E5CA2161E0107141C5CA293C9FC130F5CA3131F5C A3133F5CA2137FA25C497EB612E0A33C3E7BBD3B>II<49B648B6FC495DA2D9000390C7000313004B5D4B5DA2180714074B5DA2180F14 0F4B5DA2181F141F4B5DA2183F143F4B5DA2187F147F4B5DA218FF91B8FC96C7FCA292C7 12015B4A5DA2170313034A5DA2170713074A5DA2170F130F4A5DA2171F131F4A5DA2173F 133F4A5DA2017F157FA24A5D496C4A7EB66CB67EA3483E7BBD44>I<49B6FC5BA2D90003 13005D5DA314075DA3140F5DA3141F5DA3143F5DA3147F5DA314FF92C7FCA35B5CA31303 5CA313075CA3130F5CA3131F5CA3133F5CA2137FA25C497EB67EA3283E7BBD23>I<49B6 903807FFFE605ED9000390C7000113E04B6E13004B15FC4E5A19E002074B5A4BEC0F804E C7FC183C020F5D4B5C4D5AEF07C0021F4AC8FC4B131E5F5F023F5C9238C003E0EE07804C C9FC027F5B4B5AEEFF801581ECFF834B7FED0F7FED1E3F49017C7FECFEF89138FFE01F03 C07F491380ED000F4A805C010714074A80A21603010F815C160183131F4A6D7FA2177F01 3F825C173F017F82A24A81496C4A7EB6D8800FB512C0A261473E7BBD46>75 D<49B5933807FFFC496062D90003F0FC00505ADBBF805E1A771AEF1407033F923801CFE0 A2F1039F020FEE071F020E606F6C140E1A3F021E161C021C04385BA2F1707F143C023804 E090C7FCF001C0629126780FE0495A02705FF00700F00E0114F002E0031C5BA2F0380301 0116704A6C6C5D18E019070103ED01C00280DA03805BA2943807000F13070200020E5C5F DB03F8141F495D010E4B5CA24D133F131E011CDAF9C05CEEFB80197F013C6DB4C7FC0138 95C8FC5E01784A5C13F8486C4A5CD807FE4C7EB500F04948B512FE16E01500563E7BBD52 >77 D<49B77E18F018FC903B0003FE0003FEEF00FF4BEC7F80F03FC00207151F19E05DA2 020F16F0A25DA2141FF03FE05DA2023F16C0187F4B1580A2027FEDFF00604B495A4D5A02 FF4A5A4D5A92C7EA3FC04CB4C7FC4990B512FC17E04ACAFCA21303A25CA21307A25CA213 0FA25CA2131FA25CA2133FA25CA2137FA25C497EB67EA33C3E7BBD3E>80 DI<49B612FCEFFF8018F0 903B0003FE000FF8EF03FE4BEB00FF8419800207ED3FC05DA219E0140F5DA3021FED7FC0 5DA2F0FF80143F4B15004D5A60027F4A5A4B495A4D5AEF3F8002FF02FEC7FC92380007F8 92B512E01780499038000FE04A6D7E707E707E0103814A130083A213075CA25E130F5C5F 1603131F5CA3013F020714404A16E05F017F160119C04A01031303496C1680B6D8800113 079438FE0F009338007E1ECAEA3FFCEF07F03B407BBD42>I<92390FF001C0ED7FFE4AB5 EA0380913907F80FC791390FC003EF91391F8001FF4AC71300027E805C495A4948143EA2 495AA2010F153C5CA3011F1538A38094C7FC80A214FC6DB4FC15F015FE6DEBFFC06D14F0 6D14FC6D80143F020F7F020180EC001F150303007F167F163FA2161FA212075A5F120EA2 001E153F94C7FCA2163E003E157E167C003F15FC4B5A486C5C4B5A6D495AD87DE0EB1F80 D8F8F849C8FC017F13FE39F03FFFF8D8E00F13E048C690C9FC32427ABF33>I<48B9FCA2 5A903AFE001FF00101F89138E0007FD807E0163E49013F141E5B48C75BA2001E147FA200 1C4B131C123C003814FFA2007892C7FC12704A153C00F01738485CC716001403A25DA214 07A25DA2140FA25DA2141FA25DA2143FA25DA2147FA25DA214FFA292C9FCA25BA25CA213 03A25CEB0FFE003FB67E5AA2383D71BC41>I<001FB500F090B512F0485DA226003FF0C7 380FFC004AEC03F04A5D715A017F1503A24A5DA201FF150795C7FC91C8FCA2485E170E5B A20003161E171C5BA20007163C17385BA2000F167817705BA2001F16F05F5BA2003F1501 A2495DA2007F1503A2495DA2160794C8FC48C8FC5E160E161E6C151C163C5E5E5E6C6C13 014B5A001F4A5A6C6C011FC9FC6D133E6C6C13F83903FC07F0C6B512C0013F90CAFCEB07 F83C406FBD44>II<147E 49B47E903907C1C38090391F80EFC090383F00FF017E137F4914804848133F485AA24848 1400120F5B001F5C157E485AA215FE007F5C90C7FCA21401485C5AA21403EDF0385AA214 07EDE078020F1370127C021F13F0007E013F13E0003E137FECF3E1261F01E313C03A0F87 81E3803A03FF00FF00D800FC133E252977A72E>97 DIIII<167C4BB4FC923807C78092380F83C0ED1F 87161FED3F3FA2157EA21780EE0E004BC7FCA414015DA414035DA30103B512F8A3902600 07E0C7FCA3140F5DA5141F5DA4143F92C8FCA45C147EA414FE5CA413015CA4495AA4495A A4495A121E127F5C12FF49C9FCA2EAFE1EEAF83C1270EA7878EA3FE0EA0F802A5383BF1C >III<1478EB01 FCA21303A314F8EB00E01400AD137C48B4FC38038F80EA0707000E13C0121E121CEA3C0F 1238A2EA781F00701380A2EAF03F140012005B137E13FE5BA212015BA212035B14381207 13E0000F1378EBC070A214F0EB80E0A2EB81C01383148038078700EA03FEEA00F8163E79 BC1C>I<1507ED1FC0A2153FA31680ED0E0092C7FCADEC07C0EC3FF0EC78F8ECE07CEB01 C01303EC807EEB0700A2010E13FE5D131E131CEB3C01A201005BA21403A25DA21407A25D A2140FA25DA2141FA25DA2143FA292C7FCA25CA2147EA214FEA25CA213015CA2121C387F 03F012FF495A5C495A4848C8FCEAF83EEA707CEA3FF0EA0FC0225083BC1C>IIIIII<903903E001F890390FF807FE903A1E7C1E0F80903A1C3E3C07C0013C137801389038 E003E0EB783F017001C013F0ED80019038F07F0001E015F8147E1603000113FEA2C75AA2 0101140717F05CA20103140F17E05CA20107EC1FC0A24A1480163F010F15005E167E5E13 1F4B5A6E485A4B5A90393FB80F80DA9C1FC7FCEC0FFCEC03E049C9FCA2137EA213FEA25B A21201A25BA21203A2387FFFE0B5FCA22D3A80A72E>I<027E1360903901FF81E0903807 C1C390391F80E7C090383F00F7017E137F5B4848EB3F80485AA2485A000F15005B121F5D 4848137EA3007F14FE90C75AA3481301485CA31403485CA314074A5A127C141F007E133F 003E495A14FF381F01EF380F879F3903FF1F80EA00FC1300143F92C7FCA35C147EA314FE 5CA21301130390B512F05AA2233A77A72A>III I<137C48B4141C26038F80137EEA0707000E7F001E15FE121CD83C0F5C12381501EA781F 007001805BA2D8F03F1303140000005D5B017E1307A201FE5C5B150F1201495CA2151F00 03EDC1C0491481A2153F1683EE0380A2ED7F07000102FF13005C01F8EBDF0F0000903807 9F0E90397C0F0F1C90391FFC07F8903907F001F02A2979A731>I<017CEB01C048B4EB07 F038038F80EA0707000E01C013F8121E001C1403EA3C0F0038EC01F0A2D8781F13000070 5BA2EAF03F91C712E012005B017E130116C013FE5B1503000115805BA2ED07001203495B 150EA25DA25D1578000114706D5B0000495A6D485AD97E0FC7FCEB1FFEEB03F0252979A7 2A>I<017C167048B491387001FC3A038F8001F8EA0707000E01C015FE001E1403001CED F000EA3C0F0038177C1507D8781F4A133C00701380A2D8F03F130F020049133812005B01 7E011F14784C137013FE5B033F14F0000192C712E05BA2170100034A14C049137E170318 80A2EF070015FE170E00010101141E01F86D131C0000D9039F5BD9FC076D5A903A3E0F07 C1E0903A1FFC03FFC0902703F0007FC7FC372979A73C>I<903903F001F890390FFC07FE 90393C1E0E0F9026780F1C138001F0EBB83FD801E013F89039C007F07FEA0380000714E0 D9000F140048151C000E4AC7FCA2001E131FA2C75BA2143F92C8FCA35C147EA314FE4A13 1CA30101143C001E1538003F491378D87F811470018314F000FF5D9039077801C039FE0F 7C033A7C0E3C078027783C1E1EC7FC391FF80FFC3907E003F029297CA72A>I<137C48B4 143826038F8013FCEA0707000E7F001E1401001C15F8EA3C0F12381503D8781F14F00070 1380A2D8F03F1307020013E012005B017E130F16C013FE5B151F1201491480A2153F0003 15005BA25D157EA315FE5D00011301EBF8030000130790387C1FF8EB3FF9EB07E1EB0003 5DA21407000E5CEA3F80007F495AA24A5AD8FF0090C7FC143E007C137E00705B387801F0 383803E0381E0FC06CB4C8FCEA03F8263B79A72C>III E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg eufm10 10.95 1 /Fg 1 103 df<1302130790380FC18090381FFF00495A495A495A5CEA01C7D803C0C7FC A2487EA47F12037FA36C7EA37F1200A3003FB512C0481480B61200C648C7FCB3B15BA45B 12015BA25B12035B5BA248C8FCA21206A21A527DBD1E>102 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh cmmi6 6 11 /Fh 11 123 df<13F8D803FE1318487E48EB803048EBC060EA3C03397000E0C000601360 48EB71801431C7FCEC3300141B141EA2141CA31418A31438A214301470A45CA35CA21D21 7E9520>13 D21 D<38078003007FEB0780A2120F90 38000F00A2141EA2001E5BA25C5C48485A495A495A49C7FCEA781E1378EA79F0EA7FC000 FEC8FC12F019167C951F>23 D<0003B512FC120F5A4814F8397818180000E01338EAC030 00001330A213701360EBE070A21478EA01C0A21203EB807C0007133C143E380F003C0006 13181E167D9424>25 D<90B612FEA2903907C0007E161E4948130EA2160CA249C7FC1530 A3013EEB6000A2EC01E0EB3FFF495BEB7C01A301F85B1630A291C71260485A16C0A21501 4848EB03801507ED0F000007147FB7FC5D27227CA12D>69 D<131FEBFF8C3801E0DE3803 807E3807007C48133C121E123E003C5B127CA3485BA215401560903801E0C01278130339 3807E180391C1CF300380FF87F3807E03C1B177E9522>97 D<1338137CA2137813701300 A7EA0780EA1FC0EA38E01230EA60F0EAC1E0A3EA03C0A3EA0780A2EA0F0013041306EA1E 0CA21318121CEA1E70EA0FE0EA07800F237DA116>105 D<000F13FC381FC3FF3931C707 803861EC0301F813C0EAC1F0A213E03903C00780A3EC0F00EA0780A2EC1E041506D80F00 130C143C15181538001EEB1C70EC1FE0000CEB07801F177D9526>110 D<3801F01E3907FC7F80390E1CE1C038180F8100301383007013071260EC0380D8001EC7 FCA45BA21580003014C0397878018012F8EC030038F0FC0638E19C1C387F0FF8381E03E0 1A177D9523>120 DII E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fi cmmi9 9 18 /Fi 18 121 df13 D31 D<123C127E12FFA4127E123C0808 7A8715>58 D<123C127EB4FCA21380A2127F123D1201A412031300A25A1206120E120C12 1C5A5A126009177A8715>I<171C177EEE01FEEE07FCEE1FF0EE7FC0923801FF00ED07FC ED1FF0ED7FC04A48C7FCEC07FCEC1FF0EC7FC04948C8FCEB07FCEB1FF0EB7FC04848C9FC EA07FCEA1FF0EA7FC048CAFCA2EA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FCEB 01FF9038007FC0EC1FF0EC07FCEC01FF9138007FC0ED1FF0ED07FCED01FF9238007FC0EE 1FF0EE07FCEE01FEEE007E171C2F2E7AA93C>I<1530157815F8A215F01401A215E01403 A215C01407A21580140FA215005CA2143EA2143C147CA2147814F8A25C1301A25C1303A2 5C1307A2495AA291C7FC5BA2131E133EA2133C137CA2137813F8A25B1201A25B1203A248 5AA25B120FA290C8FC5AA2121E123EA2123C127CA2127812F8A25A12601D4B7CB726>I< EC0FF0EC7FFE91B57E903903F01FC09039078007E090390E0003F0496D7E6F7E013F147C 6E137EA2163E91C7123F133E90C8FCA31780A2EC1FC0ECFFF0903803E03C90260F800E13 0090393F00067F017E130749130348485C48487F120748485C5B121F5E485AA24B5A127F 90C7FC4B5AA25E00FE140F5E007E141F5E4BC7FCA2157E6C5C4A5A6C6C485A6C6C485A39 07E03F806CB5C8FCC613FCEB3FE029387EB529>64 D<010FB612F817FF18C0903B003FC0 003FE0EF0FF0EF03F84B6D7E717E027F157F8492C81380A24A151F19C05CA21301A25CA2 1303183F5CA2130719804A157FA2130F19004A5D60011F1501605C4D5A013F5E17074A4A 5A60017F4B5A4DC7FC91C8127E4C5A494A5AEE0FF049EC3FC000014AB4C8FCB712FC16F0 93C9FC3A337DB23F>68 D<010FB712FEA218FC903A003FC000031700187C4B143CA2027F 151C181892C8FCA25CA24A1303A201014A1338040613304A1500160E13035E4A137C91B5 12FC5B5EECF0001638130F16305C1860011F027013E0046013C04A140104001380133F17 034A15005F017F150EA291C8121E5F49157C5F4914030001ED1FF0B8FCA25F37337DB239 >I<03FF13180207EBE038021FEBF87891397F00FCF802FCEB1FF0D901F0130F49481307 49481303494814E0A249C71201A2013E15C0A3137E1780A2017F91C7FC8080EB3FF014FF 15F06D13FE6D6D7E6D806D80010080020F7F1400150F6F7E150315011500A2120CA2001C 5D1218A2150100385D003C14035E4B5A007E4A5A007F141F6D49C7FCD87BE0137C39F9FC 03F839F07FFFE0D8E01F138026C003FEC8FC2D377CB42F>83 D<267FFFFE90380FFFF8A3 000190C8EA7F0049153C1738491530A217701203491560A217E01207495DA21601120F49 5DA21603121F4992C7FCA25E123F491406A2160E127F90C8120CA2161C5A481518A21638 1630481570166016E04B5A7E007E4A5A4BC8FC007F140E6C143C6C6C5B6C6C485A3907F0 0FC06CB5C9FCC613FCEB1FE035357BB234>85 D97 D<14FE903807FF8090381F03 C090387C01E03801F800485A485A485A485A1401D83F0013C01403007EEB0F80ECFE0038 7FFFF8B5128000FCC8FCA45AA415186C1438007C147015E0003CEB01C0003EEB07806CEB 1E00380F80FC3803FFE0C690C7FC1D227DA024>101 D105 D<011F131F90397FC07FE0 9039E3E1E0F09039C3E380783A01C1F7007CD981FE133CD983FC133E00035BEB03F0163F EA0707120600025B1200010F147F167E5CA2011F14FE16FC5CA2013FEB01F8A291380003 F016E0491307ED0FC002801380ED1F009038FFC03E9038FEE0F89038FC7FE0EC1F800001 90C8FCA25BA21203A25BA21207A25BB57EA3283083A027>112 D<13F8D803FEEB01C0D8 070FEB03E0000EEB8007121C001813C00038140FEA301F0070018013C01260013F131F00 E0130000401580C65A017E133F13FE491400A25D120149137E1602EDFE0716064913FCA2 160E0201130C9039F803F81C1618000090380F7C38D97C1C137090393FF81FE0903907E0 078028227EA02C>117 D<01F0130ED803FC131FD8071EEB3F80EA0E1F121C0038EB801F 0030140F013F130700701300006014035BD8E07E14001240EA00FE495B000114065BA215 0E0003140C5B151C15181538491330157015606D13E04A5A0001495A6D48C7FC3800FC1E EB3FF8EB07E021227EA025>I<90391F801F8090397FE07FE09039E0F0E0703A01C0F9C0 F83903807D833807007F000E1403000C15F0001C137E0018EC01C002FEC7FC00385B1210 C7FC13015CA31303A25C1640010714E016C0001C5B007E1401010F148000FE1403011FEB 0700011B130E39F839F01C397070F878393FE07FE0390F801F8025227EA02C>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj cmr9 9 48 /Fj 48 122 df12 D<14C01301EB0380EB0F00130E5B133C5B5BA2485A485AA21207 5B120F90C7FC5AA2121E123EA3123C127CA55AB0127CA5123C123EA3121E121FA27E7F12 077F1203A26C7E6C7EA213787F131C7F130FEB0380EB01C01300124A79B71E>40 D<12C07E1270123C121C7E120F6C7E6C7EA26C7E6C7EA27F1378137C133C133EA2131E13 1FA37F1480A5EB07C0B0EB0F80A514005BA3131E133EA2133C137C137813F85BA2485A48 5AA2485A48C7FC120E5A123C12705A5A124A7CB71E>I<156015F0B3A4007FB812C0B912 E0A26C17C0C800F0C8FCB3A4156033327CAB3C>43 D<123C127EB4FCA21380A2127F123D 1201A412031300A25A1206120E120C121C5A5A126009177A8715>I<123C127E12FFA412 7E123C08087A8715>46 D 48 D<13075B5B137FEA07FFB5FC13BFEAF83F1200B3B3A2497E007FB51280A319327AB1 26>IIII<000C14C0380FC00F90B5128015005C5C14F014C0D80C18C7FC90C8 FCA9EB0FC0EB7FF8EBF07C380FC03F9038001F80EC0FC0120E000CEB07E0A2C713F01403 A215F8A41218127E12FEA315F0140712F8006014E01270EC0FC06C131F003C14806CEB7F 00380F80FE3807FFF8000113E038003F801D347CB126>I<1230123C003FB6FCA34814FE A215FC0070C7123800601430157015E04814C01401EC0380C7EA07001406140E5C141814 385CA25CA2495A1303A3495AA2130FA3131F91C7FCA25BA55BA9131C20347CB126>55 DI I<123C127E12FFA4127E123C1200B0123C127E12FFA4127E123C08207A9F15>I<007FB8 12C0B912E0A26C17C0CCFCAC007FB812C0B912E0A26C17C033147C9C3C>61 D 70 D72 DI80 D82 D<007FB712FEA390398007F001D87C00EC003E0078161E0070160EA20060160600E01607 A3481603A6C71500B3AB4A7E011FB512FCA330337DB237>84 D87 D91 D93 D97 DII<153FEC0FFFA3EC007F81AE EB07F0EB3FFCEBFC0F3901F003BF3907E001FF48487E48487F8148C7FCA25A127E12FEAA 127E127FA27E6C6C5BA26C6C5B6C6C4813803A03F007BFFC3900F81E3FEB3FFCD90FE013 0026357DB32B>III<151F90391FC07F809039FFF8E3C039 01F07FC73907E03F033A0FC01F83809039800F8000001F80EB00074880A66C5CEB800F00 0F5CEBC01F6C6C48C7FCEBF07C380EFFF8380C1FC0001CC9FCA3121EA2121F380FFFFEEC FFC06C14F06C14FC4880381F0001003EEB007F4880ED1F8048140FA56C141F007C15006C 143E6C5C390FC001F83903F007E0C6B51280D91FFCC7FC22337EA126>III108 D<2703F01FE013FF00FF90267FF80313C0903BF1 E07C0F03E0903BF3803E1C01F02807F7003F387FD803FE1470496D486C7EA2495CA2495C B3486C496C487EB53BC7FFFE3FFFF0A33C217EA041>I<3903F01FC000FFEB7FF09038F1 E0FC9038F3807C3907F7007EEA03FE497FA25BA25BB3486CEB7F80B538C7FFFCA326217E A02B>II<3903F03F8000FF EBFFE09038F3C0F89038F7007ED807FE7F6C48EB1F804914C049130F16E0ED07F0A3ED03 F8A9150716F0A216E0150F16C06D131F6DEB3F80160001FF13FC9038F381F89038F1FFE0 D9F07FC7FC91C8FCAA487EB512C0A325307EA02B>I<903807F00390383FFC07EBFC0F39 01F8038F3807E001000F14DF48486CB4FC497F123F90C77E5AA25A5AA9127FA36C6C5B12 1F6D5B000F5B3907E003BF3903F0073F3800F81EEB3FF8EB0FE090C7FCAAED7F8091380F FFFCA326307DA029>I<3803E07C38FFE1FF9038E38F809038E71FC0EA07EEEA03ECA290 38FC0F8049C7FCA35BB2487EB512E0A31A217FA01E>II<1330A51370A313F0A21201A212031207381FFFFEB5FCA23803 F000AF1403A814073801F806A23800FC0EEB7E1CEB1FF8EB07E0182F7FAD1E>IIII<3A7FFF807FF8A33A07F8001FC00003EC0F800001EC070015066C6C5BA26D131C 017E1318A26D5BA2EC8070011F1360ECC0E0010F5BA2903807E180A214F3010390C7FC14 FBEB01FEA26D5AA31478A21430A25CA214E05CA2495A1278D8FC03C8FCA21306130EEA70 1CEA7838EA1FF0EA0FC025307F9F29>121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmr6 6 8 /Fk 8 57 df<1438B2B712FEA3C70038C7FCB227277C9F2F>43 D<13E01201120712FF12 F91201B3A7487EB512C0A212217AA01E>49 D I<13FF000313C0380F03E0381C00F014F8003E13FC147CA2001E13FC120CC712F8A2EB01 F0EB03E0EB0FC03801FF00A2380003E0EB00F01478147C143E143F1230127812FCA2143E 48137E0060137C003813F8381E03F0380FFFC00001130018227DA01E>I<14E01301A213 031307A2130D131D13391331136113E113C1EA01811203EA07011206120C121C12181230 127012E0B6FCA2380001E0A6EB03F0EB3FFFA218227DA11E>I<00101330381E01F0381F FFE014C01480EBFE00EA1BF00018C7FCA513FE381BFF80381F03C0381C01E0381800F014 F8C71278A2147CA21230127812F8A214784813F8006013F0387001E01238381E07803807 FF00EA01F816227CA01E>II<137F3803FFC0380781E0380E00704813380018131C1238A3123C003F1338381FC0 78EBE0F0380FF9E03807FF80120114C0000713F0380F0FF8381C03FC383801FE3870007E 141F48130F1407A314060070130E0078130C6C1338001F13F03807FFC0C6130018227DA0 1E>56 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmsy6 6 2 /Fl 2 49 df0 D48 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmex8 8 1 /Fm 1 99 df<143014FCEB03FF010F13C0013F13F090387F03F83901FC00FED807E0EB1F 80D81F80EB07E0007EC7EA01F800F0EC003C00C0150C260C80B027>98 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fn msbm10 10.95 3 /Fn 3 83 df67 D78 D<007FB612FCB812C06C16F83B03E007C07FFE0000903A0F001F7F80020E9038078FC093 380383E0EFC0F0040113788484EFE00E1600180F84A760180E0401131EEFC01C183C0403 5BEF81F093380787E093381F7FC04BB5C7FC020FB512FC17C004F7C8FC91390E1C078092 381E03C0ED0E01030F7FED078003037FEEC078923801E0380300133C707EEE780EEE380F 93383C0780EE1E03040E7F93380F01E093380780F004031370EFC078706C7E04007F717E 943878078094383803C00003D90F8090383C01E0007FB500FE90381FFFFCB6806C823E3E 7EBD39>82 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo cmmi8 8 22 /Fo 22 123 df11 D<131FD9FFC013304801F0137000076D13604815 E0D9807C13C0391E003C0148011E13800038EB0E03480107130000605CEC030612E0C713 8EEC018C159C159815B815B0A215F05DA35DA25DA21403A44AC7FCA4140EA45CA3141824 2C7F9D24>13 D<13FC13FFEB1FC0130F6D7EA36D7EA2130180A26D7EA3147EA280A36E7E A2140F81A24A7E143F147FECF3F0EB01E3EB03C190380781F8130F49C67E133E5B49137E 485A48487F1207485A4848EB1F8048C7FC127E48EC0FC048EC07E000701403232F7DAD29 >21 D23 D<14C0A5ECFFE04913F8130790381F9FE0017F C7FC13FE5B485A12035B1207A25BA312037FA23801FBFE38007FFFA2EBF7FED803C0C7FC 485A48C8FC121EA25A127C1278A212F85A7EA37EB4FCEA7FC0EA3FF8EA1FFE380FFFC000 0313F038007FFCEB1FFEEB03FF1300141F80A3EB701EEB3C1CEB1FF8EB03E01D3C7EAD1F >I<90B612F812035A4815F03A1E0380C000003C130000701301130700E05CEAC0063800 0E03A3131CA2133C140713381378A201F07FA21201A2D803E07FA20007130313C0A26C48 6C5A251E7E9C29>I<123C127EB4FCA21380A2127F123D1201A312031300A25A1206120E 5A5A5A126009157A8714>59 D<15C0140114031580A214071500A25C140EA2141E141CA2 143C143814781470A214F05CA213015CA213035C130791C7FCA25B130EA2131E131CA213 3C1338A21378137013F05BA212015BA212035BA2120790C8FC5A120EA2121E121CA2123C 1238A212781270A212F05AA21A437CB123>61 D<147F903801FFE090380780F890380E00 3C497F497F49148001781307017C14C001FC130316E0A2137090C7FC16F0A314FE903807 FF8390381F01C390397C00E7E049137748481337D807E0133F49131F484814C0121F48C7 FCA2481580127EA2ED3F0012FE48147EA2157C15FC5D4A5A007C495AA26C495A001E49C7 FC6C133E3807C0F83803FFE038007F8024307DAE25>64 D<013FB71280A2D900FEC7127F 170F4A1407A20101150318005CA21303A25C16300107147094C7FC4A136016E0130F1501 9138C007C091B5FC5BECC0074A6C5AA2133FA20200EB000CA249151C92C71218017E1538 173001FE15705F5B4C5A000115034C5A49140F161F00034AB4C7FCB8FC5E312D7DAC34> 69 D<90273FFFFC0FB5FCA2D900FEC7EA3F80A24A1500A201015D177E5CA2010315FE5F 5CA2010714015F5CA2010F14035F5C91B6FC5B9139C00007E05CA2013F140F5F91C7FCA2 49141F5F137EA201FE143F94C7FC5BA200015D167E5BA2000315FEB539E03FFFF8A2382D 7CAC3A>72 D<913807F00691383FFE0E9138F80F9E903903E001FE903807800049C7127C 131E49143CA2491438A313F81630A26D1400A27FEB7F8014F86DB47E15F06D13FC01077F 01007F141F02011380EC003F151F150FA215071218A3150F00381500A2151EA2007C5C00 7E5C007F5C397B8003E039F1F00F8026E07FFEC7FC38C00FF0272F7CAD2B>83 D<1307EB0F80EB1FC0A2EB0F80EB070090C7FCA9EA01E0EA07F8EA0E3CEA1C3E12381230 1270EA607EEAE07C12C013FC485A120012015B12035BA21207EBC04014C0120F13801381 381F01801303EB0700EA0F06131EEA07F8EA01F0122E7EAC18>105 D<131FEA03FFA2EA003FA2133EA2137EA2137CA213FCA25BA2120115F89038F003FCEC0F 0E0003EB1C1EEC387EEBE07014E03807E1C09038E3803849C7FC13CEEA0FDC13F8A2EBFF 80381F9FE0EB83F0EB01F81300481404150C123EA2007E141C1518007CEBF038ECF83000 FC1470EC78E048EB3FC00070EB0F801F2F7DAD25>107 D<27078007F0137E3C1FE01FFC 03FF803C18F0781F0783E03B3878E00F1E01263079C001B87F26707F8013B00060010013 F001FE14E000E015C0485A4914800081021F130300015F491400A200034A13076049133E 170F0007027EEC8080188149017C131F1801000F02FCEB3F03053E130049495C180E001F 0101EC1E0C183C010049EB0FF0000E6D48EB03E0391F7E9D3E>109 D<3907C007E0391FE03FF83918F8783E393879E01E39307B801F38707F00126013FEEAE0 FC12C05B00815C0001143E5BA20003147E157C5B15FC0007ECF8081618EBC00115F0000F 1538913803E0300180147016E0001F010113C015E390C7EAFF00000E143E251F7E9D2B> I<90387C01F89038FE07FE3901CF8E0F3A03879C0780D907B813C0000713F000069038E0 03E0EB0FC0000E1380120CA2D8081F130712001400A249130F16C0133EA2017EEB1F80A2 017C14005D01FC133E5D15FC6D485A3901FF03E09038FB87C0D9F1FFC7FCEBF0FC000390 C8FCA25BA21207A25BA2120FA2EAFFFCA2232B829D24>112 D<130E131FA25BA2133EA2 137EA2137CA213FCA2B512F8A23801F800A25BA21203A25BA21207A25BA2120FA25BA200 1F1310143013001470146014E0381E01C0EB0380381F0700EA0F0EEA07FCEA01F0152B7E A919>116 DI<013F137C9038FFC1FF3A01C1E383803A0380F703C0390700F6 0F000E13FE4813FC12180038EC0700003049C7FCA2EA200100005BA313035CA301075B5D 14C000385CD87C0F130600FC140E011F130C011B131C39F03BE038D8707113F0393FE0FF C0260F803FC7FC221F7E9D28>120 DI<011E1330EB3F809038FFC07048EBE0E0ECF1C03803C0FF90 38803F80903800070048130EC75A5C5C5C495A495A49C7FC131E13385B491340484813C0 485A38070001000EEB0380380FE007391FF81F0038387FFF486C5A38601FFC38E00FF038 C003C01C1F7D9D21>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmsy8 8 8 /Fp 8 122 df0 D<140381B3A3B812FCA3C7D80380C7FCB3B812 FCA32E2F7CAD37>6 DI<170EA3170F8384170384170184717E1878187C84180FF007C0BA12F819 FC19F8CBEA07C0F00F00183E601878604D5A60170360170795C7FC5F170EA33E237CA147 >33 D<137813FE1201A3120313FCA3EA07F8A313F0A2EA0FE0A313C0121F1380A3EA3F00 A3123E127E127CA35AA35A0F227EA413>48 DI<18031807 180F180E181E181C183C18381878187018F018E01701EF03C01880170718005F170E171E 171C173C17381778177017F05F16015F16035F160701C092C7FC486C5C0007151E486C14 1C003F153CD873F8143800E31578D801FC147016F06C6C5C1501017F5C1503D93F805B15 07D91FC090C8FC5D90380FE00E151E903807F01C153C903803F83815786D6C5A5DEB00FF 5D147F5D143F92C9FC80141E140E38427C823B>112 D<1338137CA81338A7007C137CB5 12FEA3387C387C00001300A5137CB3A41338AD173D7CAE20>121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq cmex10 10.95 21 /Fq 21 115 df<140E141E143C147814F01301EB03E0EB07C0A2EB0F80EB1F00A2133E13 7E137C13FC5B1201A2485AA3485AA2120F5BA2121FA25BA2123FA390C7FCA25AA6127E12 FEB3A4127E127FA67EA27FA3121FA27FA2120FA27F1207A26C7EA36C7EA212007F137C13 7E133E7FA2EB0F80EB07C0A2EB03E0EB01F013001478143C141E140E176C72832A>0 D<12E07E12787E7E121F6C7E6C7EA26C7E6C7EA26C7E7F137C137E133E133FA2EB1F80A3 EB0FC0A214E01307A214F0A21303A214F8A31301A214FCA6130014FEB3A414FC1301A614 F8A21303A314F0A21307A214E0A2130F14C0A2EB1F80A3EB3F00A2133E137E137C13FC5B 485AA2485A485AA2485A48C7FC121E5A5A5A5A176C7C832A>II I<12F0B3B3B3A5043B73811E>12 D16 D<12F07E127C7E7E6C7E6C7E7F6C7E6C7E1200 7F137E7FA26D7E6D7EA26D7EA26D7E6D7EA26D7EA280147E147F80A26E7EA281140FA281 140781A21403A281A2140181A3140081A4157E157FA5811680A9ED1FC0B3A9ED3F80A916 005DA5157E15FEA45D1401A35D1403A25DA21407A25D140F5DA2141F5DA24AC7FCA25C14 7E14FE5CA2495AA2495A495AA2495AA2495A49C8FCA2137E5B5B1201485A485A5B485A48 C9FC123E5A5A5A22A37D8336>I<17F01601EE03E0EE07C0EE0F80EE1F00163E5E16FC4B 5A4B5A4B5A5E150F4B5A4BC7FCA2157E5D14015D4A5AA24A5A140F5D141F5D143F4AC8FC A214FEA2495AA2495AA2495AA3495AA2495AA3495AA349C9FCA25B5BA312015BA21203A2 5BA21207A25BA2120FA35BA2121FA45BA2123FA65B127FAA48CAFCB3AE6C7EAA123F7FA6 121FA27FA4120FA27FA31207A27FA21203A27FA21201A27F1200A37F7FA26D7EA36D7EA3 6D7EA26D7EA36D7EA26D7EA26D7EA2147FA26E7E141F81140F8114076E7EA26E7E811400 157E81A26F7E6F7E1507826F7E6F7E6F7E167C8282EE0F80EE07C0EE03E0EE01F016002C DA6D8343>I<12F07E127C7E7E6C7E6C7E6C7E7F6C7E6C7E137E133E133F6D7E6D7EA26D 7E6D7E8013016D7EA2147E147F8081141F816E7EA26E7EA26E7EA26E7EA26E7EA3157FA2 6F7EA36F7EA36F7EA2821507A3821503A282A21501A282A21500A282A382A21780A4163F A217C0A6161F17E0AAEE0FF0B3AEEE1FE0AA17C0163FA61780A2167FA41700A25EA35EA2 1501A25EA21503A25EA215075EA3150F5EA24B5AA34B5AA34BC7FCA215FEA34A5AA24A5A A24A5AA24A5AA24A5A5D143F92C8FC5C147E5CA2495A13035C495A495AA2495A49C9FC13 3E137E5B485A485A5B485A485A48CAFC123E5A5A5A2CDA7D8343>III<1778EE01F81607161FEE7FE0EEFF8003031300ED07FC4B 5A4B5A4B5A4B5A4B5A93C7FC4A5A14035D14075D140F5DA34A5AB3B3B3A9143F5DA2147F 5DA24AC8FCA2495A13035C495A495A495A495A495A49C9FC485AEA07F8485AEA3FC0B4CA FC12FCA2B4FCEA3FC0EA0FF06C7EEA01FE6C7E6D7E6D7E6D7E6D7E6D7E6D7E8013016D7E A26E7EA281143FA281141FB3B3B3A96E7EA38114078114038114016E7E826F7E6F7E6F7E 6F7E6F7E6FB4FC03001380EE7FE0EE1FF816071601EE00782DDA758344>26 D<12F012FCB47E7FEA3FF0EA0FFCEA03FE6C7E6C13C0EB3FE06D7E6D7E6D7E1303806D7E 7F81147F81143FA381141FB3B3B3A881140FA36E7EA26E7EA26E7EA26E7E6F7E82153F6F 7E6F7E6F7EED01FE6F7EEE7F80EE1FE0EE07F81601A21607EE1FE0EE7F80EEFF004B5AED 07F84B5A4B5A4B5A157F5E4BC7FC4A5AA24A5AA24A5AA24A5AA3141F5DB3B3B3A8143F5D A3147F5D14FF92C8FC5B495A5C1307495A495A495AEBFFC04890C9FC485AEA0FFCEA3FF0 EAFFC05B00FCCAFC12F02DDA758344>I73 D88 D90 D<1560EC01F84A7EEC0FFF023F13C091B512F049EB0FF8903907FC03FE90 3A1FF000FF80D97FC0EB3FE04848C7EA0FF8D803FCEC03FCD80FF0EC00FFD83F80ED1FC0 00FEC9EA07F00078EE01E00060EE0060341181C333>98 D<160F167FED01FF1507ED1FFC ED7FE0EDFF804A1300EC03FC4A5A4A5A4A5A4A5A5D147F92C7FCA25C5CB3B3AA13015CA2 13035C13075C495A131F495A495A49C8FCEA03FC485AEA1FE0EA7FC048C9FC12FCB4FCEA 7FC0EA1FE0EA07F86C7EC6B4FC6D7E6D7E6D7E130F6D7E801303801301A2801300B3B3AA 8080A281143F816E7E6E7E6E7E6E7E6EB4FC6E1380ED7FE0ED1FFCED07FF1501ED007F16 0F28A376833D>110 D<12F012FE6C7E13E0EA3FF8EA0FFCEA03FEC66C7E6D7E6D7E131F 6D7E6D7E130380130180A21300B3B3AA8080A281143F816E7E140F6E7E81EC01FC6EB4FC ED7F80ED1FE0ED0FF8ED03FEED00FF163F16FFED03FEED0FF8ED1FE0ED7F80EDFF00EC01 FCEC07F85D4A5A141F4A5A5D147F92C7FCA25C5CB3B3AA1301A25C13035C1307495A495A 133F495A495AD803FEC8FCEA0FFCEA3FF8EAFFE0138048C9FC12F028A376833D>I<1CC0 F301E01B03A2F307C0A2F30F80A2F31F00A21B3EA263A263A2505AA2631A03A2505AA250 5AA250C7FCA21A3EA262A262A24F5AA24F5AA24F5AA24F5AA24FC8FCA2193EA261A261A2 4E5AA24E5AA2611807131801384C5A137CD801FC4CC9FC487E0007173EEA1EFF00385F5A 486C6C5D12006D6C4A5AA26D6C4A5AA24D5A6D7E4D5A6D7E4DCAFC6D7E173EA26D6C5CA2 6D6C5CA26E6C485AA24C5AEC3FC04C5AEC1FE05F91380FF00FA24CCBFCEC07F8163EEC03 FC5EEC01FE5EA26E6C5AA26F5AA26F5AA25E151F93CCFC150E536D76835B>I<1CC0F301 E0A21B03A21CC0A21B07A21C80A31B0FA21C00A263A21B1EA21B3EA21B3CA21B7CA21B78 A21BF8A263A31A01A263A21A03A263A21A07A263A21A0FA298C7FCA262A21A1EA31A3EA2 1A3CA21A7CA21A78A21AF8A262A21901A262A31903A262A21907A262A2190FA297C8FCA2 61A2191EA2193EA2193CA3197CA21978A219F8A261A21801A261A21803A261A21807A201 085F1318A20138160F137C96C9FC13FC00015FA2486C161E1207183E120FD80CFF163C5A 0038177C123048177838E07F8012C0000017F8A2606D7E1701A2606D7E1703A260A26D6C 1407A260A2170F6D7E95CAFCA36D6C5CA2171EA2173E6D7E173CA2177CA26D6C1478A217 F8A26E6C5BA31601A2DA3FC05BA21603A25FEC1FE01607A25FEC0FF0160FA294CBFCA26E 6C5AA2161EA3913803FC3EA2163CA2913801FE7CA21678A216F8EC00FF5EA46F5AA46F5A A56F5AA493CCFC81150E53DB76835B>114 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fr cmsy10 10.95 18 /Fr 18 113 df<007FB812FEBAFCA26C17FE3804799847>0 D<121EEA7F80A2EAFFC0A4 EA7F80A2EA1E000A0A799B19>I<1506150FB3A9007FB912E0BA12F0A26C18E0C8000FC9 FCB3A6007FB912E0BA12F0A26C18E03C3C7BBB47>6 D<007FB912E0BA12F0A26C18E0C8 000FC9FCB3A6007FB912E0BA12F0A26C18E0C8000FC9FCB3A915063C3C7BAD47>I<180E 183F18FFEF03FEEF0FF8EF3FE0EFFF80933803FE00EE0FF8EE3FE0EEFF80DB03FEC7FCED 0FF8ED7FE0913801FF80DA07FEC8FCEC1FF8EC7FC04948C9FCEB07FCEB1FF0EB7FC04848 CAFCEA07FCEA1FF0EA7FC048CBFCA2EA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07 FCEB01FF9038007FC0EC1FF0EC07FE913801FF809138007FE0ED1FF8ED03FE923800FF80 EE3FE0EE0FF8EE03FE933800FF80EF3FE0EF0FF8EF03FEEF00FF183F180E1800AE007FB8 12FEBAFCA26C17FE384879B947>20 D<127012FCB4FCEA7FC0EA1FF0EA07FCEA01FF3800 7FC0EB1FF0EB07FCEB01FF9038007FC0EC1FF0EC07FE913801FF809138007FE0ED1FF8ED 03FE923800FF80EE3FE0EE0FF8EE03FE933800FF80EF3FE0EF0FF8EF03FEEF00FFA2EF03 FEEF0FF8EF3FE0EFFF80933803FE00EE0FF8EE3FE0EEFF80DB03FEC7FCED0FF8ED7FE091 3801FF80DA07FEC8FCEC1FF8EC7FC04948C9FCEB07FCEB1FF0EB7FC04848CAFCEA07FCEA 1FF0EA7FC048CBFC12FC1270CCFCAE007FB812FEBAFCA26C17FE384879B947>I24 D<0203B612FE023F15FF91B8FC010316FED90FFEC9FCEB1FE0EB7F8001FECAFC EA01F8485A485A485A5B48CBFCA2123EA25AA21278A212F8A25AA87EA21278A2127CA27E A27EA26C7E7F6C7E6C7E6C7EEA00FEEB7F80EB1FE0EB0FFE0103B712FE010016FF143F02 0315FE383679B147>26 D<19301978A2197C193CA2193E191EA2191F737EA2737E737EA2 737E737E1A7C1A7EF21F80F20FC0F207F0007FBB12FCBDFCA26C1AFCCDEA07F0F20FC0F2 1F80F27E001A7C624F5A4F5AA24F5A4F5AA24FC7FC191EA2193E193CA2197C1978A21930 50307BAE5B>33 D49 D<0203B512F8023F14FC91B6FC010315F8D90FFE C8FCEB1FE0EB7F8001FEC9FCEA01F8485A485A485A5B48CAFCA2123EA25AA21278A212F8 A25AA2B812F817FCA217F800F0CAFCA27EA21278A2127CA27EA27EA26C7E7F6C7E6C7E6C 7EEA00FEEB7F80EB1FE0EB0FFE0103B612F8010015FC143F020314F82E3679B13D>I72 D83 D85 D<146014F01301A214E01303A214C01307A2 EB0F80A214005BA2131E133EA25BA2137813F8A25B1201A25B1203A2485AA25B120FA290 C7FC5AA2123EA2123C127CA2127812F8A41278127CA2123C123EA27EA27E7FA212077FA2 6C7EA212017FA212007FA21378137CA27FA2131E131FA27F1480A2EB07C0A2130314E0A2 130114F0A213001460145A77C323>104 D<126012F07EA21278127CA2123C123EA27EA2 7E7FA212077FA26C7EA212017FA212007FA21378137CA27FA2131E131FA27F1480A2EB07 C0A2130314E0A2130114F0A414E01303A214C01307A2EB0F80A214005BA2131E133EA25B A2137813F8A25B1201A25B1203A2485AA25B120FA290C7FC5AA2123EA2123C127CA21278 12F8A25A1260145A7BC323>I<126012F0B3B3B3B3B11260045B76C319>I<1A061A0F1A1F A21A3EA21A7CA21AF8A2F101F0A2F103E0A2F107C0A2F10F80A2F11F00A2193EA261A261 A24E5AA24E5AA24E5AA24E5AA24EC7FCA2183EA260A260A24D5AA24D5A133801F85E486C 15071203D80FFE4B5A121D00394CC8FCEAF1FF00C0163EC67F017F5D80013F5D80011F4A 5A80010F4A5A8001074A5AA26E495A13036E49C9FC13016E133E7F6F5A147F6F5A143FED E1F0141FEDE3E015F391380FF7C015FF6E5BA26E90CAFCA26E5AA26E5AA215781570485B 7A834C>112 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmmi10 10.95 46 /Fs 46 123 df11 D13 DI17 D<133F14E0EB07F0EB03FC13016D7EA3147FA26E7EA36E7EA36E7EA36E7EA36E7E A26E7EA36E7EA3157FA36F7E157F15FF4A7F5C913807CFE0EC0F8FEC1F0F91383E07F014 7C14FC49486C7EEB03F0EB07E049486C7EEB1F80EB3F00496D7E13FE4848147F485A485A 4848EC3F80485A123F4848EC1FC048C8FC4816E048150F48ED07F0007015032C407BBE35 >21 D<017FEC01C0D83FFFEC03E016075B1200160F17C05B161F00011680163F491500A2 0003157EA2495C150100075D4B5A49495AA2000F4A5A4B5A4949C7FC157E001F147C5D49 485AEC07E0003F495A4AC8FCEB003E14F848485AEB07C0D87E1FC9FC13FCEAFFE0138000 F8CAFC2B287CA72D>23 DI<011FB612FE017F15FF48B8FC5A4816FE3B 0FC03801C000EA1F00003E1403003C01785B4813705AECF0075AC712E0010191C7FCA25D EB03C0A313071480A2010F5BA2EB1F0082A2133EA2137E825B150F0001815B120315075B C648EB038030287DA634>I<020FB512FE027F14FF49B7FC1307011F15FE903A3FE03FE0 0090387F000F01FE6D7E4848130348488048481301485A5B121F5B123F90C7FC5A127EA2 150300FE5D5AA24B5AA2150F5E4B5AA2007C4AC7FC157E157C6C5C001E495A001FEB07E0 390F800F802603E07EC8FC3800FFF8EB3FC030287DA634>27 D<1678A21670A216F0A25E A21501A25EA21503A25EA21507A293C7FCA25DA2150EEDFFC0020F13FC91383F9E3F903A 01F81C0FC0D903E0EB03E0903A0FC03C01F0D91F00EB00F8017E0138137C5B4848017813 3E485A48480170133F120F4901F0131F485A5D48C7FC0201143F5A007E5CA20203147F00 FE167E485C17FE020714FC1601007C020013F8EE03F0007E49EB07E0A2003E010EEB0FC0 003FED1F806C011EEB3F00D80F80147C3A07C01C01F8D803E0EB03E03A01F03C1F80D800 7E01FEC7FC90381FFFF801011380D90078C8FCA21470A214F0A25CA21301A25CA21303A2 5CA21307A230527CBE36>30 D<13FE2603FF80157026078FE015F0260F07F01401000E6D 15E00103ED03C0000C6DEC0780D80001ED0F006E141E01005D5F027F5C4C5A91383F8003 5F4C5A6E6C48C7FC161E5E6E6C5A5EEDE1E0913807E3C015F75E6EB4C8FC5D5D5D6E7EA2 140314074A7EA2141EEC3C7F147814F049486C7EEB03C0EB078049486C7EA2131E496D7E 5B498048481307485A48486D7E48C7FC48EDFC03001E0201EB07804803FE1300486E6C5A 48ED7F1E0060ED1FFCC9EA03F0343B7EA739>II<012016E00178ED03F801F8ED07FC12015B485A5B0007160349150148CA FC187C121EA2001C173C003C021C14380038147EA20078177803FE147000705CA218F04B 14E000F001011401A24B14C017034B1307020315806C496C130FEF1F006CD91FF85B007C 496C137E007E496C5B3A7F83FE7F87263FFFFCEBFFF84A6C5B6C01F05C6CD9C01F5B6CD9 000790C7FCD801FCEB01F836297FA739>I39 D<121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A0A798919>58 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A312011380120313005A 120E5A1218123812300B1C798919>I<180E183F18FFEF03FEEF0FF8EF3FE0EFFF809338 03FE00EE0FF8EE3FE0EEFF80DB03FEC7FCED1FF8ED7FE0913801FF80DA07FEC8FCEC1FF0 EC7FC04948C9FCEB07FCEB1FF0EB7FC04848CAFCEA07FCEA1FF0EA7FC048CBFCA2EA7FC0 EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FCEB01FF9038007FC0EC1FF0EC07FE913801 FF809138007FE0ED1FF8ED03FE923800FF80EE3FE0EE0FF8EE03FE933800FF80EF3FE0EF 0FF8EF03FEEF00FF183F180E383679B147>II<127012FCB4FCEA7FC0EA1FF0EA07 FCEA01FF38007FC0EB1FF0EB07FCEB01FF9038007FC0EC1FF8EC07FE913801FF80913800 7FE0ED0FF8ED03FE923800FF80EE3FE0EE0FF8EE03FE933800FF80EF3FE0EF0FF8EF03FE EF00FFA2EF03FEEF0FF8EF3FE0EFFF80933803FE00EE0FF8EE3FE0EEFF80DB03FEC7FCED 0FF8ED7FE0913801FF80DA07FEC8FCEC1FF8EC7FC04948C9FCEB07FCEB1FF0EB7FC04848 CAFCEA07FCEA1FF0EA7FC048CBFC12FC1270383679B147>I<15FF020713E091381F00F8 0278133E4A7F4948EB0F804948EB07C04948EB03E091C7FC496CEB01F002E014F8131F16 0017FCA25C0107C812FE90C9FCA7EC03FCEC3FFF9138FE03C1903903F000E149481371D9 1F80133149C7123B017EEC1BFC5B0001151F4848140F484815F8A2485A121F17F0485A16 1F17E0127F5BEE3FC0A200FF168090C8127F1700A216FEA2484A5A5E007E1403007F4A5A 5E6C4A5A6C6C495A4BC7FC6C6C13FE6C6C485A3903F80FF06CB512C06C6C90C8FCEB0FF8 2F437CC030>64 D67 D<49B712F818FF19C0D9000190C7EA3FF0F00FF84BEC03FCF000FE197F0203EE3F805DF1 1FC0A20207EE0FE05D1AF0A2020F16075DA21AF8141F5DA2190F143F5DA21AF0147F4B15 1FA302FF17E092C9123FA21AC049177F5C1A8019FF010318005C4E5A61010716034A5E4E 5A180F010F4C5A4A5E4E5A4EC7FC011F16FE4A4A5AEF07F8013FED0FE0EF3FC04A49B4C8 FC017FEC0FFCB812F017C004FCC9FC453E7DBD4B>I<49B912C0A3D9000190C71201F000 3F4B151F190F1A80020316075DA314075D1A00A2140F4BEB0380A205075B021FED000E4B 92C7FC5FA2023F141E5D173EEE01FE4AB55AA3ED800102FF6D5A92C71278A34915705C19 1C05F0133C01034B13384A167894C71270A2010717F04A5E180161010F16034A4B5AA218 0F011F4CC7FC4A5D187E013F16FE4D5A4A140F017F15FFB95AA260423E7DBD43>I<49B9 FCA3D9000190C7120718004B157F193F191E14035DA314075D191CA2140F5D17074D133C 021F020E13384B1500A2171E023F141C4B133C177C17FC027FEB03F892B5FCA39139FF80 03F0ED00011600A2495D5CA2160101035D5CA293C9FC13075CA3130F5CA3131F5CA2133F A25C497EB612F8A3403E7DBD3A>I<49B6D8C03FB512F81BF01780D900010180C7383FF0 0093C85B4B5EA2197F14034B5EA219FF14074B93C7FCA260140F4B5DA21803141F4B5DA2 1807143F4B5DA2180F4AB7FC61A20380C7121F14FF92C85BA2183F5B4A5EA2187F13034A 5EA218FF13074A93C8FCA25F130F4A5DA21703131F4A5DA2013F1507A24A5D496C4A7EB6 D8E01FB512FCA2614D3E7DBD4C>72 D<49B612F0A3D900010180C7FC93C8FC5DA314035D A314075DA3140F5DA3141F5DA3143F5DA3147F5DA314FF92C9FCA35B5C180C181E010316 1C5C183C183813074A1578187018F0130F4AEC01E0A21703011FED07C04A140F171F013F ED3F8017FF4A1303017F021F1300B9FCA25F373E7DBD3E>76 D<49B56C49B512F81BF0A2 90C76D9039000FFE004AEE03F0705D735A03DF150302037F038F5E82190791380787FC03 0793C7FC1503705C140F91260E01FF140EA26F151E021E80021C017F141C83193C023C6D 7E02381638161F711378147802706D6C1370A2040714F002F0804A01035C8318010101EC 01FF4A5E82188313034A91387FC380A2EF3FC7010716E791C8001F90C8FC18F718FF4981 010E5E1707A2131E011C6F5AA2013C1501137C01FE6F5AEA03FFB512FC187818704D3E7D BD49>78 D<49B712F018FF19C0D9000190C76C7EF00FF84BEC03FC1801020382727E5DA2 14071A805DA2140F4E13005DA2021F5E18034B5D1807023F5E4E5A4B4A5A4E5A027F4B5A 06FEC7FC4BEB03FCEF3FF091B712C005FCC8FC92CBFCA25BA25CA21303A25CA21307A25C A2130FA25CA2131FA25CA2133FA25C497EB612E0A3413E7DBD3A>80 D<49B77E18F818FFD90001D900017F9438003FE04BEC0FF0727E727E14034B6E7EA30207 825DA3020F4B5A5DA24E5A141F4B4A5A614E5A023F4B5A4B4A5A06FEC7FCEF03FC027FEC 0FF04BEBFF8092B500FCC8FC5F9139FF8001FE92C7EA7F80EF1FC084496F7E4A1407A284 13035CA2170F13075C60171F130F5CA3011F033F5B4AEE038018E0013F17071A004A021F 5B496C160EB600E090380FF01E05075B716C5ACBEAFFE0F03F8041407DBD45>82 DI<48B912FCA25A913A0003FE000F01F84A1301 D807E0EE00F8491307491778000F5D90C7FC001E140FA2001C4B1470123C0038141FA200 785D1270033F15F000F018E0485DC81600157FA25EA215FFA293C9FCA25CA25DA21403A2 5DA21407A25DA2140FA25DA2141FA25DA2143FA25DA2147FA214FF497F001FB612FCA25E 3E3D7FBC35>I<007FB500F090387FFFFE19FC5D26007FE0C7000313804A913800FC004A 5D187001FF16F0A291C95AA2481601605BA200031603605BA20007160795C7FC5BA2000F 5E170E5BA2001F161E171C5BA2003F163C17385BA2007F1678A2491570A200FF16F0A290 C95AA216015F5A16035F16074CC8FC160E161E5E007F5D5E6C4A5A6D495A6C6C495A6C6C 011FC9FC6C6C137E3903FC03F8C6B512E0013F1380D907FCCAFC3F407ABD3E>II100 DI<163EEEFFC0923803 E1E0923807C0F0ED0F811687ED1F8F160F153FA217E092387E038093C7FCA45DA514015D A30103B512FCA390260003F0C7FCA314075DA4140F5DA5141F5DA4143F92C8FCA45C147E A414FE5CA413015CA4495AA35CEA1E07127F5C12FF495AA200FE90C9FCEAF81EEA703EEA 7878EA1FF0EA07C02C537CBF2D>I<143C14FEA21301A314FCEB00701400AD137E3801FF 803803C7C0EA0703000F13E0120E121C13071238A2EA780F007013C0A2EAF01F14801200 133F14005B137EA213FE5BA212015B0003130E13F0A20007131EEBE01CA2143CEBC03814 78147014E013C13803E3C03801FF00EA007C173E7EBC1F>105 D107 D110 D112 D<147014FC1301A25CA21303A25CA21307A25CA2130FA25CA2007FB512F0B6FC15E03900 1F8000133FA291C7FCA25BA2137EA213FEA25BA21201A25BA21203A25BA21207EC01C013 E01403000F1480A2EBC0071500140E141E5C000713385C3803E1E03801FF80D8003EC7FC 1C3A7EB821>116 D<137C48B4EC03802603C7C0EB0FC0EA0703000F7F000E151F121C01 0715801238163FEA780F0070491400A2D8F01F5C5C0000157E133F91C712FEA2495C137E 150113FE495CA215030001161C4914F0A21507173CEEE038150F031F1378000016706D13 3F017C017313F0017E01E313E0903A3F03C1F1C0903A0FFF007F80D901FCEB1F002E297E A734>I<017E147848B4EB01FC2603C7C013FED807031303000F13E0120E121C01071301 00381400167ED8780F143E00705B161EEAF01F4A131C1200133F91C7123C16385B137E16 7801FE14705B16F016E0120149EB01C0A2ED0380A2ED0700A20000140E5D6D133C017C5B 6D5B90381F03C0903807FF80D901FCC7FC27297EA72C>I120 D<137C48B4EC03802603C7C0EB0FC0EA0703000F7F000E151F001C168013071238163FD8 780F150000705BA2D8F01F5C4A137E1200133F91C712FE5E5B137E150113FE495CA21503 00015D5BA215075EA2150F151F00005D6D133F017C137F017E13FF90393F03DF8090380F FF1FEB01FC90C7123F93C7FCA25DD80380137ED80FE013FE001F5C4A5AA24848485A4A5A 6CC6485A001C495A001E49C8FC000E137C380781F03803FFC0C648C9FC2A3B7EA72D>I< 02F8130ED903FE131ED90FFF131C49EB803C49EBC0784914F090397E07F1E09038F800FF 49EB1FC049EB07800001EC0F006C48131E90C75A5D5D4A5A4A5A4A5A4AC7FC143E14785C 495A495A495A49C8FC011E14E05B5B4913014848EB03C0485AD807F8EB078048B4131F3A 1F87E07F00391E03FFFE486C5B00785CD870005B00F0EB7FC048011FC7FC27297DA72A> I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft cmr8 8 18 /Ft 18 119 df<013FB5FCA29038007F806EC8FCA6903801FFE0011F13FE90397F3F3F80 D801F8EB07E0D807E0EB01F8D80FC06D7ED81F80147ED83F0080481680A2007E151F00FE 16C0A5007E1680007F153FA26C1600D81F80147ED80FC05CD807E0495AD801F8EB07E0D8 007FEB3F8090261FFFFEC7FC010113E0D9003FC8FCA64A7E013FB5FCA22A2D7CAC33>8 D<13031307130E131C1338137013F0EA01E013C01203EA0780A2EA0F00A2121EA35AA45A A512F8A25AAB7EA21278A57EA47EA37EA2EA0780A2EA03C0120113E0EA00F01370133813 1C130E1307130310437AB11B>40 D<12C07E12707E7E7E120FEA0780120313C0EA01E0A2 EA00F0A21378A3133CA4131EA5131FA2130FAB131FA2131EA5133CA41378A313F0A2EA01 E0A2EA03C013801207EA0F00120E5A5A5A5A5A10437CB11B>I43 D48 D<130C133C137CEA03FC12FFEAFC7C1200B3B113FE387FFFFEA2172C7AAB23>III<140EA2141E143EA2147E14FEA2EB01BE1303143E13 06130E130C131813381330136013E013C0EA0180120313001206120E120C5A123812305A 12E0B612FCA2C7EA3E00A9147F90381FFFFCA21E2D7EAC23>I<000CEB0180380FC01F90 B512005C5C14F014C0D80C7EC7FC90C8FCA8EB1FC0EB7FF8380DE07C380F801F01001380 000E130F000CEB07C0C713E0A2140315F0A4127812FCA448EB07E012E0006014C0007013 0F6C14806CEB1F006C133E380780F83801FFE038007F801C2D7DAB23>II61 D<15F8141FA214011400ACEB0FE0EB7FF83801F81E3803E0073807C003380F8001EA1F00 481300123E127EA25AA9127C127EA2003E13017EEB8003000F13073903E00EFC3A01F03C FFC038007FF090391FC0F800222F7EAD27>100 DI104 D<3807C0FE39FFC3FF809038C7 03E0390FDE01F0EA07F8496C7EA25BA25BB2486C487E3AFFFE1FFFC0A2221E7E9D27> 110 DI<3AFFFC01FFC0A23A0FE0007E000007147C15 380003143015706C6C1360A26C6C5BA390387C0180A26D48C7FCA2EB3F07EB1F06A2EB0F 8CA214DCEB07D8A2EB03F0A36D5AA26D5A221E7F9C25>118 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fu cmbx12 14.4 36 /Fu 36 122 df44 D46 D<157815FC14031407141F14FF130F0007B5FCB6FCA2147F13F0EAF800C7 FCB3B3B3A6007FB712FEA52F4E76CD43>49 DI<9138 0FFFC091B512FC0107ECFF80011F15E090263FF8077F9026FF800113FC4848C76C7ED803 F86E7E491680D807FC8048B416C080486D15E0A4805CA36C17C06C5B6C90C75AD801FC16 80C9FC4C13005FA24C5A4B5B4B5B4B13C04B5BDBFFFEC7FC91B512F816E016FCEEFF80DA 000713E0030113F89238007FFE707E7013807013C018E07013F0A218F8A27013FCA218FE A2EA03E0EA0FF8487E487E487EB57EA318FCA25E18F891C7FC6C17F0495C6C4816E001F0 4A13C06C484A1380D80FF84A13006CB44A5A6CD9F0075BC690B612F06D5D011F15800103 02FCC7FCD9001F1380374F7ACD43>I<177C17FEA2160116031607160FA2161F163F167F A216FF5D5DA25D5DED1FBFED3F3F153E157C15FCEC01F815F0EC03E01407EC0FC01580EC 1F005C147E147C5C1301495A495A5C495A131F49C7FC133E5B13FC485A5B485A1207485A 485A90C8FC123E127E5ABA12C0A5C96C48C7FCAF020FB712C0A53A4F7CCE43>III<171F4D7E4D7EA24D7EA34C7FA24C7FA34C7FA34C7FA24C 7FA34C8083047F80167E8304FE804C7E03018116F8830303814C7E03078116E083030F81 4C7E031F81168083033F8293C77E4B82157E8403FE824B800201835D840203834B800207 835D844AB87EA24A83A3DA3F80C88092C97E4A84A2027E8202FE844A82010185A24A8201 03854A82010785A24A82010F855C011F717FEBFFFCB600F8020FB712E0A55B547BD366> 65 D<932601FFFCEC01C0047FD9FFC013030307B600F81307033F03FE131F92B8EA803F 0203DAE003EBC07F020F01FCC7383FF0FF023F01E0EC0FF94A01800203B5FC494848C9FC 4901F8824949824949824949824949824990CA7E494883A2484983485B1B7F485B481A3F A24849181FA3485B1B0FA25AA298C7FC5CA2B5FCAE7EA280A2F307C07EA36C7FA21B0F6C 6D1980A26C1A1F6C7F1C006C6D606C6D187EA26D6C606D6D4C5A6D6D16036D6D4C5A6D6D 4C5A6D01FC4C5A6D6DEE7F806D6C6C6C4BC7FC6E01E0EC07FE020F01FEEC1FF80203903A FFE001FFF0020091B612C0033F93C8FC030715FCDB007F14E0040101FCC9FC525479D261 >67 D69 D73 D82 D<91260FFF80130791B5 00F85B010702FF5B011FEDC03F49EDF07F9026FFFC006D5A4801E0EB0FFD4801800101B5 FC4848C87E48488149150F001F824981123F4981007F82A28412FF84A27FA26D82A27F7F 6D93C7FC14C06C13F014FF15F86CECFF8016FC6CEDFFC017F06C16FC6C16FF6C17C06C83 6C836D826D82010F821303010082021F16801400030F15C0ED007F040714E01600173F05 0F13F08383A200788200F882A3187FA27EA219E07EA26CEFFFC0A27F6D4B13806D17006D 5D01FC4B5A01FF4B5A02C04A5A02F8EC7FF0903B1FFFC003FFE0486C90B65AD8FC0393C7 FC48C66C14FC48010F14F048D9007F90C8FC3C5479D24B>I97 D<913801FFF8021FEBFF8091B612F00103 15FC010F9038C00FFE903A1FFE0001FFD97FFC491380D9FFF05B4817C048495B5C5A485B A2486F138091C7FC486F1300705A4892C8FC5BA312FFAD127F7FA27EA2EF03E06C7F1707 6C6D15C07E6E140F6CEE1F806C6DEC3F006C6D147ED97FFE5C6D6CEB03F8010F9038E01F F0010390B55A01001580023F49C7FC020113E033387CB63C>99 D<4DB47E0407B5FCA5EE 001F1707B3A4913801FFE0021F13FC91B6FC010315C7010F9038E03FE74990380007F7D9 7FFC0101B5FC49487F4849143F484980485B83485B5A91C8FC5AA3485AA412FFAC127FA3 6C7EA37EA26C7F5F6C6D5C7E6C6D5C6C6D49B5FC6D6C4914E0D93FFED90FEFEBFF80903A 0FFFC07FCF6D90B5128F0101ECFE0FD9003F13F8020301C049C7FC41547CD24B>I<9138 03FFC0023F13FC49B6FC010715C04901817F903A3FFC007FF849486D7E49486D7E484913 0F48496D7E48178048497F18C0488191C7FC4817E0A248815B18F0A212FFA490B8FCA318 E049CAFCA6127FA27F7EA218E06CEE01F06E14037E6C6DEC07E0A26C6DEC0FC06C6D141F 6C6DEC3F806D6CECFF00D91FFEEB03FE903A0FFFC03FF8010390B55A010015C0021F49C7 FC020113F034387CB63D>IIII<137F497E000313E0487FA2487FA76C5BA26C5BC613806DC7 FC90C8FCADEB3FF0B5FCA512017EB3B3A6B612E0A51B547BD325>I107 DIII<913801FFE0 021F13FE91B612C0010315F0010F9038807FFC903A1FFC000FFED97FF86D6C7E49486D7F 48496D7F48496D7F4A147F48834890C86C7EA24883A248486F7EA3007F1880A400FF18C0 AC007F1880A3003F18006D5DA26C5FA26C5F6E147F6C5F6C6D4A5A6C6D495B6C6D495B6D 6C495BD93FFE011F90C7FC903A0FFF807FFC6D90B55A010015C0023F91C8FC020113E03A 387CB643>I<903A3FF001FFE0B5010F13FE033FEBFFC092B612F002F301017F913AF7F8 007FFE0003D9FFE0EB1FFFC602806D7F92C76C7F4A824A6E7F4A6E7FA2717FA285187F85 A4721380AC1A0060A36118FFA2615F616E4A5BA26E4A5B6E4A5B6F495B6F4990C7FC03F0 EBFFFC9126FBFE075B02F8B612E06F1480031F01FCC8FC030313C092CBFCB1B612F8A541 4D7BB54B>I<90397FE003FEB590380FFF80033F13E04B13F09238FE1FF89139E1F83FFC 0003D9E3E013FEC6ECC07FECE78014EF150014EE02FEEB3FFC5CEE1FF8EE0FF04A90C7FC A55CB3AAB612FCA52F367CB537>114 D<903903FFF00F013FEBFE1F90B7FC120348EB00 3FD80FF81307D81FE0130148487F4980127F90C87EA24881A27FA27F01F091C7FC13FCEB FFC06C13FF15F86C14FF16C06C15F06C816C816C81C681013F1580010F15C01300020714 E0EC003F030713F015010078EC007F00F8153F161F7E160FA27E17E07E6D141F17C07F6D EC3F8001F8EC7F0001FEEB01FE9039FFC00FFC6DB55AD8FC1F14E0D8F807148048C601F8 C7FC2C387CB635>I<143EA6147EA414FEA21301A313031307A2130F131F133F13FF5A00 0F90B6FCB8FCA426003FFEC8FCB3A9EE07C0AB011FEC0F8080A26DEC1F0015806DEBC03E 6DEBF0FC6DEBFFF86D6C5B021F5B020313802A4D7ECB34>IIII<007FB500F090387FFFFEA5C66C48C7000F90C7FC6D6CEC07 F86D6D5C6D6D495A6D4B5A6F495A6D6D91C8FC6D6D137E6D6D5B91387FFE014C5A6E6C48 5A6EEB8FE06EEBCFC06EEBFF806E91C9FCA26E5B6E5B6F7E6F7EA26F7F834B7F4B7F92B5 FCDA01FD7F03F87F4A486C7E4A486C7E020F7FDA1FC0804A486C7F4A486C7F02FE6D7F4A 6D7F495A49486D7F01076F7E49486E7E49486E7FEBFFF0B500FE49B612C0A542357EB447 >II E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fv cmr10 10.95 84 /Fv 84 125 df0 D<010FB612E0A3D900030180C7FCDA 00FEC8FCA8913807FFC0027F13FC903A03FCFE7F80D90FE0EB0FE0D93F80EB03F8D9FE00 EB00FE4848157F4848ED3F804848ED1FC0000F17E04848ED0FF0003F17F8A24848ED07FC A200FF17FEA8007F17FCA26C6CED0FF8A2001F17F06C6CED1FE0000717C06C6CED3F806C 6CED7F006C6C15FED93F80EB03F8D90FE0EB0FE0D903FCEB7F809027007FFFFCC7FC0207 13C0DA00FEC8FCA8913803FF80010FB612E0A3373E7BBD42>8 D<4AB4EB0FE0021F9038 E03FFC913A7F00F8FC1ED901FC90383FF03FD907F090397FE07F80494801FF13FF494848 5BD93F805C137F0200ED7F00EF003E01FE6D91C7FC82ADB97EA3C648C76CC8FCB3AE486C 4A7E007FD9FC3FEBFF80A339407FBF35>11 D<4AB4FC021F13C091387F01F0903901FC00 78D907F0131C4948133E494813FF49485A137F1400A213FE6F5A163893C7FCAA167FB8FC A33900FE00018182B3AC486CECFF80007FD9FC3F13FEA32F407FBF33>I<4AB47E021F13 F791387F00FFEB01F8903807F001EB0FE0EB1FC0EB3F80137F14008101FE80AEB8FCA3C6 48C77EB3AE486CECFF80007FD9FC3F13FEA32F407FBF33>I<4AB4ECFF80021FD9C00F13 E0913B7F01F03F80F8903C01F80078FE003CD907F0D93FF8130E49484948131F49484948 EB7F804948484913FF137F02005CA201FE92C7FC6FED7F0070141C96C7FCAAF13F80BBFC A3C648C76CC7FC197F193FB3AC486C4A6CEB7FC0007FD9FC3FD9FE1FB5FCA348407FBF4C >I<133E133F137F13FFA2EA01FEEA03FCEA07F813F0EA0FE0EA1FC01380EA3E005A5A12 70122010116EBE2D>19 D<121EEA7F80EAFFC0A9EA7F80ACEA3F00AC121EAB120CC7FCA8 121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A4179C019>33 D<121EEA7F8012FF13C0A213 E0A3127FEA1E601200A413E013C0A312011380120313005A120E5A1218123812300B1C79 BE19>39 D<1430147014E0EB01C0EB03801307EB0F00131E133E133C5B13F85B12015B12 03A2485AA2120F5BA2121F90C7FCA25AA3123E127EA6127C12FCB2127C127EA6123E123F A37EA27F120FA27F1207A26C7EA212017F12007F13787F133E131E7FEB07801303EB01C0 EB00E014701430145A77C323>I<12C07E12707E7E121E7E6C7E7F12036C7E7F12007F13 78137CA27FA2133F7FA21480130FA214C0A3130714E0A6130314F0B214E01307A614C013 0FA31480A2131F1400A25B133EA25BA2137813F85B12015B485A12075B48C7FC121E121C 5A5A5A5A145A7BC323>I<1506150FB3A9007FB912E0BA12F0A26C18E0C8000FC9FCB3A9 15063C3C7BB447>43 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A3 12011380120313005A120E5A1218123812300B1C798919>II<12 1EEA7F80A2EAFFC0A4EA7F80A2EA1E000A0A798919>IIIII I<150E151E153EA2157EA215FE1401A21403EC077E1406140E141CA214381470A214E0EB 01C0A2EB0380EB0700A2130E5BA25B5BA25B5B1201485A90C7FC5A120E120C121C5AA25A 5AB8FCA3C8EAFE00AC4A7E49B6FCA3283E7EBD2D>I<00061403D80780131F01F813FE90 B5FC5D5D5D15C092C7FC14FCEB3FE090C9FCACEB01FE90380FFF8090383E03E090387001 F8496C7E49137E497F90C713800006141FC813C0A216E0150FA316F0A3120C127F7F12FF A416E090C7121F12FC007015C012780038EC3F80123C6CEC7F00001F14FE6C6C485A6C6C 485A3903F80FE0C6B55A013F90C7FCEB07F8243F7CBC2D>II<1238123C123F90B612FCA316F85A16F016E00078C712010070 EC03C0ED078016005D48141E151C153C5DC8127015F04A5A5D14034A5A92C7FC5C141EA2 5CA2147C147814F8A213015C1303A31307A3130F5CA2131FA6133FAA6D5A0107C8FC2640 7BBD2D>III<121EEA7F80A2EAFFC0A4EA7F80A2EA1E00C7 FCB3121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A2779A619>I<121EEA7F80A2EAFFC0A4 EA7F80A2EA1E00C7FCB3121E127FEAFF80A213C0A4127F121E1200A412011380A3120313 005A1206120E120C121C5A1230A20A3979A619>I<007FB912E0BA12F0A26C18E0CDFCAE 007FB912E0BA12F0A26C18E03C167BA147>61 D<15074B7EA34B7EA34B7EA34B7EA34B7E 15E7A2913801C7FC15C3A291380381FEA34AC67EA3020E6D7EA34A6D7EA34A6D7EA34A6D 7EA34A6D7EA349486D7E91B6FCA249819138800001A249C87EA24982010E157FA2011E82 011C153FA2013C820138151FA2017882170F13FC00034C7ED80FFF4B7EB500F0010FB512 F8A33D417DC044>65 DIIIIIIII<011FB512FCA3D9000713006E 5A1401B3B3A6123FEA7F80EAFFC0A44A5A1380D87F005B007C130700385C003C495A6C49 5A6C495A2603E07EC7FC3800FFF8EB3FC026407CBD2F>IIII< B56C91B512F88080D8007F030713006EEC01FC6E6E5A1870EB77FCEB73FEA2EB71FF0170 7FA26E7E6E7EA26E7E6E7EA26E7E6E7EA26E7E6E7FA26F7E6F7EA26F7E6F7EA26F7E6F7E A26F7E6F1380A2EE7FC0EE3FE0A2EE1FF0EE0FF8A2EE07FCEE03FEA2EE01FF7013F0A217 7F173FA2171F170FA2170701F81503487ED807FF1501B500F81400A218703D3E7DBD44> III< ED7FE0913807FFFE91391FC03F8091397F000FE0D901FCEB03F8D907F0EB00FE4948147F 49486E7E49486E7E49C86C7E498248486F7E49150300038348486F7EA2000F834981001F 1880A24848EE7FC0A3007F18E0A249163FA200FF18F0AC007F18E0A26D167FA3003F18C0 A26C6CEEFF80A3000F18006D5D0007DA0F805B6C6C90393FE003FCED70706C6C496C485A 6C6C48486C485A017FD9800E5BD93F819038061FC0D91FC19038073F80D90FE14AC7FCD9 07F1EB03FE902601FDC013F8903A007EE007E091271FF03FC013180207B5FC9139007FE1 E0DB0001143883711378A2706C13F0EFFF0318FFA27113E0A37113C0711380711300715A EF01F83D527BBF47>III< 003FB91280A3903AF0007FE001018090393FC0003F48C7ED1FC0007E1707127C00781703 A300701701A548EF00E0A5C81600B3B14B7E4B7E0107B612FEA33B3D7DBC42>IIII89 D91 D93 D<121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A0A79BD19> 95 DIII<49B4FC010F13E090383F00F8017C131E484813 1F4848137F0007ECFF80485A5B121FA24848EB7F00151C007F91C7FCA290C9FC5AAB6C7E A3003FEC01C07F001F140316806C6C13076C6C14000003140E6C6C131E6C6C137890383F 01F090380FFFC0D901FEC7FC222A7DA828>IIII<167C903903F8 01FF903A1FFF078F8090397E0FDE1F9038F803F83803F001A23B07E000FC0600000F6EC7 FC49137E001F147FA8000F147E6D13FE00075C6C6C485AA23901F803E03903FE0FC02607 1FFFC8FCEB03F80006CAFC120EA3120FA27F7F6CB512E015FE6C6E7E6C15E06C81000381 3A0FC0001FFC48C7EA01FE003E140048157E825A82A46C5D007C153E007E157E6C5D6C6C 495A6C6C495AD803F0EB0FC0D800FE017FC7FC90383FFFFC010313C0293D7EA82D>II< EA01E0EA07F8A2487EA46C5AA2EA01E0C8FCACEA01FC127FA3120712031201B3AC487EB5 12F0A3143E7DBD1A>I<1478EB01FEA2EB03FFA4EB01FEA2EB00781400AC147FEB7FFFA3 13017F147FB3B3A5123E127F38FF807E14FEA214FCEB81F8EA7F01387C03F0381E07C038 0FFF803801FC00185185BD1C>III<2701F801FE14FF00FF902707FFC00313E0913B1E07E00F03F0913B7803F03C01F8 0007903BE001F87000FC2603F9C06D487F000101805C01FBD900FF147F91C75B13FF4992 C7FCA2495CB3A6486C496CECFF80B5D8F87FD9FC3F13FEA347287DA74C>I<3901F801FE 00FF903807FFC091381E07E091387803F000079038E001F82603F9C07F0001138001FB6D 7E91C7FC13FF5BA25BB3A6486C497EB5D8F87F13FCA32E287DA733>I<14FF010713E090 381F81F890387E007E01F8131F4848EB0F804848EB07C04848EB03E0000F15F04848EB01 F8A2003F15FCA248C812FEA44815FFA96C15FEA36C6CEB01FCA3001F15F86C6CEB03F0A2 6C6CEB07E06C6CEB0FC06C6CEB1F80D8007EEB7E0090383F81FC90380FFFF0010090C7FC 282A7EA82D>I<3901FC03FC00FF90381FFF8091387C0FE09039FDE003F03A07FFC001FC 6C496C7E6C90C7127F49EC3F805BEE1FC017E0A2EE0FF0A3EE07F8AAEE0FF0A4EE1FE0A2 EE3FC06D1580EE7F007F6E13FE9138C001F89039FDE007F09039FC780FC0DA3FFFC7FCEC 07F891C9FCAD487EB512F8A32D3A7EA733>I<02FF131C0107EBC03C90381F80F090397F 00387C01FC131CD803F8130E4848EB0FFC150748481303121F485A1501485AA448C7FCAA 6C7EA36C7EA2001F14036C7E15076C6C130F6C7E6C6C133DD8007E137990383F81F19038 0FFFC1903801FE0190C7FCAD4B7E92B512F8A32D3A7DA730>I<3901F807E000FFEB1FF8 EC787CECE1FE3807F9C100031381EA01FB1401EC00FC01FF1330491300A35BB3A5487EB5 12FEA31F287EA724>I<90383FC0603901FFF8E03807C03F381F000F003E1307003C1303 127C0078130112F81400A27E7E7E6D1300EA7FF8EBFFC06C13F86C13FE6C7F6C14800001 14C0D8003F13E0010313F0EB001FEC0FF800E01303A214017E1400A27E15F07E14016C14 E06CEB03C0903880078039F3E01F0038E0FFFC38C01FE01D2A7DA824>I<131CA6133CA4 137CA213FCA2120112031207001FB512C0B6FCA2D801FCC7FCB3A215E0A912009038FE01 C0A2EB7F03013F138090381F8700EB07FEEB01F81B397EB723>IIIIII<001FB61280A2EBE0000180140049485A001E495A121C4A5A 003C495A141F00385C4A5A147F5D4AC7FCC6485AA2495A495A130F5C495A90393FC00380 A2EB7F80EBFF005A5B484813071207491400485A48485BA248485B4848137F00FF495A90 B6FCA221277EA628>I124 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fw cmbx10 10.95 39 /Fw 39 122 df12 D40 D<127012F8127C7EEA3F806C7E6C7E12076C7E7F6C7E6C7EA2137F8013 3F806D7EA280130FA280130780A36D7EA4807FA51580B01500A55B5CA4495AA35C130F5C A2131F5CA2495A5C137F91C7FC13FEA2485A485A5B485A120F485A485A003EC8FC5A5A12 70195A7AC329>I48 D<140F143F5C495A130F48 B5FCB6FCA313F7EAFE071200B3B3A8B712F0A5243C78BB34>I<903803FF80013F13F890 B512FE00036E7E4881260FF80F7F261FC0037F4848C67F486C6D7E6D6D7E487E6D6D7EA2 6F1380A46C5A6C5A6C5A0007C7FCC8FC4B1300A25E153F5E4B5AA24B5A5E4A5B4A5B4A48 C7FC5D4A5AEC1FE04A5A4A5A9139FF000F80EB01FC495A4948EB1F00495AEB1F8049C7FC 017E5C5B48B7FC485D5A5A5A5A5AB7FC5EA4293C7BBB34>I<903801FFE0010F13FE013F 6D7E90B612E04801817F3A03FC007FF8D807F06D7E82D80FFC131F6D80121F7FA56C5A5E 6C48133FD801F05CC8FC4B5A5E4B5A4A5B020F5B902607FFFEC7FC15F815FEEDFFC0D900 0113F06E6C7E6F7E6F7E6F7E1780A26F13C0A217E0EA0FC0487E487E487E487EA317C0A2 5D491580127F49491300D83FC0495A6C6C495A3A0FFE01FFF86CB65A6C5DC61580013F49 C7FC010313E02B3D7CBB34>II<00071538D80FE0EB01F801FE133F90B6FC5E5E5E5E93C7FC5D15F85D15C04AC8FC 0180C9FCA9ECFFC0018713FC019F13FF90B67E020113E09039F8007FF0496D7E01C06D7E 5B6CC77FC8120F82A31780A21207EA1FC0487E487E12FF7FA21700A25B4B5A6C5A01805C 6CC7123F6D495AD81FE0495A260FFC075B6CB65A6C92C7FCC614FC013F13F0010790C8FC 293D7BBB34>II<121F7F13F8 90B712F0A45A17E017C0178017005E5E5A007EC7EA01F84B5A007C4A5A4B5A4B5A93C7FC 485C157E5DC7485A4A5AA24A5A140F5D141F143F5D147FA214FF92C8FC5BA25BA3495AA3 130FA5131FAA6D5A6D5A6D5A2C3F7ABD34>II<903801FFE0 010F13FC013F13FF90B612C04801E07F489038003FF048486D7E000F6E7E485A6F7E123F 48488081178012FFA217C0A517E0A4007F5CA4003F5C6C7E5D6C7E00075C3903FF80FB6C 13FF6C6C13F36D13C3010F018313C090380008031400A24B1380EA03F0487E486C150048 7E4B5AA25E151F4B5A495C6C48EBFFE049485B2607FC0F5B6CB6C7FC6C14FC6C14F06D13 C0D90FFEC8FC2B3D7CBB34>II<922607FFC0130E92B500FC131E020702FF133E023FEDC07E91B7EAE1FE 01039138803FFB499039F80003FF4901C01300013F90C8127F4948151FD9FFF8150F4849 1507485B4A1503481701485B18004890CAFC197E5A5B193E127FA349170012FFAC127F7F 193EA2123FA27F6C187E197C6C7F19FC6C6D16F86C6D150119F06C6D15036C6DED07E0D9 7FFEED0FC06D6CED3F80010F01C0ECFF006D01F8EB03FE6D9039FF801FFC010091B55A02 3F15E002071580020002FCC7FC030713C03F407ABE4C>67 D75 D77 D80 D<903A03FFC001C0011FEBF803017FEBFE0748B6128F4815DF 48010013FFD80FF8130F48481303497F4848EB007F127F49143F161F12FF160FA27F1607 A27F7F01FC91C7FCEBFF806C13F8ECFFC06C14FCEDFF806C15E016F86C816C816C816C16 806C6C15C07F010715E0EB007F020714F0EC003F1503030013F8167F163F127800F8151F A2160FA27EA217F07E161F6C16E06D143F01E015C001F8EC7F8001FEEB01FF9026FFE007 13004890B55A486C14F8D8F81F5CD8F00314C027E0003FFEC7FC2D407ABE3A>83 D<003FB912FCA5903BFE003FFE003FD87FF0EE0FFE01C0160349160190C71500197E127E A2007C183EA400FC183F48181FA5C81600B3AF010FB712F8A5403D7CBC49>I<903807FF C0013F13F848B6FC48812607FE037F260FF8007F6DEB3FF0486C806F7EA36F7EA26C5A6C 5AEA01E0C8FC153F91B5FC130F137F3901FFFE0F4813E0000F1380381FFE00485A5B485A 12FF5BA4151F7F007F143F6D90387BFF806C6C01FB13FE391FFF07F36CEBFFE100031480 C6EC003FD91FF890C7FC2F2B7DA933>97 D<13FFB5FCA512077EAFEDFFE0020713FC021F EBFF80027F80DAFF8113F09139FC003FF802F06D7E4A6D7E4A13074A80701380A218C082 A318E0AA18C0A25E1880A218005E6E5C6E495A6E495A02FCEB7FF0903AFCFF01FFE0496C B55AD9F01F91C7FCD9E00713FCC7000113C033407DBE3A>IIII<13FFB5FCA512077EAFED1FF8EDFFFE02036D7E4A80DA0FE07F91381F007F023C805C 4A6D7E5CA25CA35CB3A4B5D8FE0FB512E0A5333F7CBE3A>104 D II<13FFB5FCA512077EB3B3 AFB512FCA5163F7CBE1D>108 D<01FFD91FF8ECFFC0B590B5010713F80203DAC01F13FE 4A6E487FDA0FE09026F07F077F91261F003FEBF8010007013EDAF9F0806C0178ECFBC04A 6DB4486C7FA24A92C7FC4A5CA34A5CB3A4B5D8FE07B5D8F03FEBFF80A551297CA858>I< 01FFEB1FF8B5EBFFFE02036D7E4A80DA0FE07F91381F007F0007013C806C5B4A6D7E5CA2 5CA35CB3A4B5D8FE0FB512E0A533297CA83A>II<01FFEBFFE0B5000713FC021FEBFF80027F80DAFF8113F09139FC007FF800 0701F06D7E6C496D7E4A130F4A6D7E1880A27013C0A38218E0AA4C13C0A318805E18005E 6E5C6E495A6E495A02FCEBFFF0DAFF035B92B55A029F91C7FC028713FC028113C00280C9 FCACB512FEA5333B7DA83A>I<3901FE01FE00FF903807FF804A13E04A13F0EC3F1F9138 7C3FF8000713F8000313F0EBFFE0A29138C01FF0ED0FE091388007C092C7FCA391C8FCB3 A2B6FCA525297DA82B>114 D<90383FFC1E48B512BE000714FE5A381FF00F383F800148 C7FC007E147EA200FE143EA27E7F6D90C7FC13F8EBFFE06C13FF15C06C14F06C806C806C 806C80C61580131F1300020713C014000078147F00F8143F151F7EA27E16806C143F6D14 0001E013FF9038F803FE90B55A15F0D8F87F13C026E00FFEC7FC222B7DA929>III119 D121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fx cmr10 10 32 /Fx 32 122 df<121C127FEAFF80A213C0A3127F121C1200A412011380A2120313005A12 06120E5A5A5A12600A1979B917>39 D<146014E0EB01C0EB0380EB0700130E131E5B5BA2 5B485AA2485AA212075B120F90C7FCA25A121EA2123EA35AA65AB2127CA67EA3121EA212 1F7EA27F12077F1203A26C7EA26C7E1378A27F7F130E7FEB0380EB01C0EB00E014601352 78BD20>I<12C07E12707E7E7E120F6C7E6C7EA26C7E6C7EA21378A2137C133C133E131E A2131F7FA21480A3EB07C0A6EB03E0B2EB07C0A6EB0F80A31400A25B131EA2133E133C13 7C1378A25BA2485A485AA2485A48C7FC120E5A5A5A5A5A13527CBD20>I45 D<121C127FEAFF80A5EA7F00121C0909798817>I<1538A3157CA315FEA34A 7EA34A6C7EA202077FEC063FA2020E7FEC0C1FA2021C7FEC180FA202387FEC3007A20270 7FEC6003A202C07F1501A2D901807F81A249C77F167FA20106810107B6FCA24981010CC7 121FA2496E7EA3496E7EA3496E7EA213E0707E1201486C81D80FFC02071380B56C90B512 FEA3373C7DBB3E>65 D71 D<003FB812E0A3D9C003EB001F273E0001FE130348EE01F00078160000701770A3006017 30A400E01738481718A4C71600B3B0913807FF80011FB612E0A335397DB83C>84 D87 D97 DIIII<147E903803FF8090380FC1E0EB1F8790383F0FF0137EA213 FCA23901F803C091C7FCADB512FCA3D801F8C7FCB3AB487E387FFFF8A31C3B7FBA19>I< ED03F090390FF00FF890393FFC3C3C9039F81F707C3901F00FE03903E007C03A07C003E0 10000FECF000A248486C7EA86C6C485AA200075C6C6C485A6D485A6D48C7FC38073FFC38 060FF0000EC9FCA4120FA213C06CB512C015F86C14FE6CECFF804815C03A0F80007FE048 C7EA0FF0003E140348140116F8481400A56C1401007C15F06CEC03E0003F1407D80F80EB 0F80D807E0EB3F003901FC01FC39007FFFF0010790C7FC26387EA52A>III107 DI<2703F00FF0EB1FE000FFD93FFCEB7FF8913AF03F01E07E903B F1C01F83803F3D0FF3800FC7001F802603F70013CE01FE14DC49D907F8EB0FC0A2495CA3 495CB3A3486C496CEB1FE0B500C1B50083B5FCA340257EA445>I<3903F00FF000FFEB3F FCECF03F9039F1C01F803A0FF3800FC03803F70013FE496D7EA25BA35BB3A3486C497EB5 00C1B51280A329257EA42E>II<3903F01FE000FFEB7FF89038F1E07E 9039F3801F803A0FF7000FC0D803FEEB07E049EB03F04914F849130116FC150016FEA316 7FAA16FEA3ED01FCA26DEB03F816F06D13076DEB0FE001F614C09039F7803F009038F1E0 7E9038F0FFF8EC1FC091C8FCAB487EB512C0A328357EA42E>I<3807E01F00FFEB7FC090 38E1E3E09038E387F0380FE707EA03E613EE9038EC03E09038FC0080491300A45BB3A248 7EB512F0A31C257EA421>114 DI<1318A51338A31378A313F8120112031207001FB5FCB6FCA2D801 F8C7FCB215C0A93800FC011580EB7C03017E13006D5AEB0FFEEB01F81A347FB220>IIIIII E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fy cmbx10 10 7 /Fy 7 117 df65 D97 D<13FFB5FCA412077EAF4AB47E020F13F0023F13FC9138FE03FFDAF000 13804AEB7FC00280EB3FE091C713F0EE1FF8A217FC160FA217FEAA17FCA3EE1FF8A217F0 6E133F6EEB7FE06E14C0903AFDF001FF80903AF8FC07FE009039F03FFFF8D9E00F13E0D9 C00390C7FC2F3A7EB935>I<903801FFC0010F13FC017F13FFD9FF8013802603FE0013C0 48485AEA0FF8121F13F0123F6E13804848EB7F00151C92C7FC12FFA9127FA27F123FED01 E06C7E15036C6CEB07C06C6C14806C6C131FC69038C07E006DB45A010F13F00101138023 257DA42A>I<9038FE03F000FFEB0FFEEC3FFF91387C7F809138F8FFC000075B6C6C5A5C A29138807F80ED3F00150C92C7FC91C8FCB3A2B512FEA422257EA427>114 D<90383FF0383903FFFEF8000F13FF381FC00F383F0003007E1301007C130012FC15787E 7E6D130013FCEBFFE06C13FCECFF806C14C06C14F06C14F81203C614FC131F9038007FFE 140700F0130114007E157E7E157C6C14FC6C14F8EB80019038F007F090B512C000F81400 38E01FF81F257DA426>I<130FA55BA45BA25B5BA25A1207001FEBFFE0B6FCA3000390C7 FCB21578A815F86CEB80F014816CEBC3E090383FFFC06D1380903803FE001D357EB425> I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fz cmr12 12 38 /Fz 38 123 df<131F1480133F137FA2EBFF00485A485A5B485A485A138048C7FC123E12 3C5A12E0124011126CC431>19 D<13FEA4EBFFC0EB0FF0EB03F8EB01FCEB00FEA5EB01FC EB07F8EB3FF0B512C0EBF8001712747D2B>24 D<121EEA7F8012FF13C0A213E0A3127FEA 1E601200A413E013C0A312011380120313005A1206120E5A5A5A12600B1D78891B>44 DI<121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A0A78891B>I<16 18163C167CA2167816F8A216F01501A216E01503A216C01507A21680150FA2ED1F00A215 1E153EA2153C157CA2157815F8A25D1401A24A5AA25D1407A25D140FA292C7FC5CA2141E 143EA2143C147CA25CA25C1301A25C1303A25C1307A25C130FA291C8FC5BA2133EA2133C 137CA2137813F8A25B1201A25B1203A2485AA25B120FA290C9FC5AA2121E123EA2123C12 7CA2127812F8A25A126026647BCA31>I<14FF010713E090381F81F890383E007C01FC13 3F4848EB1F8049130F4848EB07C04848EB03E0A2000F15F0491301001F15F8A2003F15FC A390C8FC4815FEA54815FFB3A46C15FEA56D1301003F15FCA3001F15F8A26C6CEB03F0A3 6C6CEB07E0000315C06D130F6C6CEB1F806C6CEB3F00013E137C90381F81F8903807FFE0 010090C7FC28447CC131>I<143014F013011303131F13FFB5FC13E713071200B3B3B049 7E497E007FB6FCA3204278C131>I<000615C0D807C0130701FCEB7F8090B612005D5D5D 15E0158026063FFCC7FC90C9FCAE14FF010713C090381F01F090383800FC01F0137ED807 C07F49EB1F8016C090C7120F000615E0C8EA07F0A316F81503A216FCA5123E127F487EA4 16F890C712075A006015F0A20070140F003015E00038EC1FC07E001EEC3F806CEC7F006C 6C13FE6C6C485A3901F807F039007FFFE0011F90C7FCEB07F826447BC131>53 D<121CA2EA1F8090B712C0A3481680A217005E0038C8120C0030151C00705D0060153016 705E5E4814014B5A4BC7FCC81206150E5D151815385D156015E04A5AA24A5A140792C8FC 5CA25C141E143EA2147E147CA214FCA21301A3495AA41307A6130FAA6D5AEB01C02A457B C231>55 D<14FF010713E0011F13F890387F00FE01FC133FD801F0EB1F804848EB0FC049 EB07E00007EC03F048481301A290C713F8481400A47FA26D130116F07F6C6CEB03E013FC 6C6CEB07C09039FF800F806C9038C01F006CEBF03EECF87839007FFEF090383FFFC07F01 077F6D13F8497F90381E7FFFD97C1F1380496C13C02601E00313E048486C13F000079038 007FF84848EB3FFC48C7120F003EEC07FE150148140016FF167F48153FA2161FA56C151E 007C153EA2007E153C003E157C6C15F86DEB01F06C6CEB03E06C6CEB07C0D803F8EB1F80 C6B4EBFF0090383FFFFC010F13F00101138028447CC131>I67 DI71 D73 D78 D80 D<003FB912F8A3903BF0001FF8001F01806D481303003EC7150048187C0078183CA20070 181CA30060180CA5481806A5C81600B3B3A54B7EED7FFE49B77EA33F447DC346>84 D I97 D99 D<167FED3FFFA315018182B3EC7F80903803 FFF090380FC07C90383F000E017E1307496D5AD803F87F48487F5B000F81485AA2485AA2 127FA290C8FC5AAB7E7FA2123FA26C7EA2000F5D7F6C6C5B00035C6C6C9038077F806C6C 010E13C0013F011C13FE90380FC0F8903803FFE09026007F0013002F467DC436>III104 DI107 DI<3901FC01FE00 FF903807FFC091381E07F091383801F8000701707F0003EBE0002601FDC07F5C01FF147F 91C7FCA25BA35BB3A8486CECFF80B5D8F83F13FEA32F2C7DAB36>110 DI<3901FC03FC00FF90380FFF8091383C07 E091387001F83A07FDE000FE00030180137FD801FFEC3F8091C7EA1FC04915E049140F17 F0160717F8160317FCA3EE01FEABEE03FCA3EE07F8A217F0160F6D15E0EE1FC06D143F17 806EEB7E00D9FDC05B9039FCF003F891383C0FE091381FFF80DA03FCC7FC91C9FCAE487E B512F8A32F3F7DAB36>I<3903F803F000FFEB1FFCEC3C3EEC707F0007EBE0FF3803F9C0 00015B13FBEC007E153C01FF13005BA45BB3A748B4FCB512FEA3202C7DAB26>114 D<90383FE0183901FFFC383907E01F78390F0003F8001E1301481300007C1478127800F8 1438A21518A27EA27E6C6C13006C7E13FC383FFFE06C13FC6C13FF6C14C06C14E0C614F0 011F13F81300EC0FFC140300C0EB01FE1400157E7E153EA27EA36C143C6C147C15786C14 F86CEB01F039F38003E039F1F00F8039E07FFE0038C00FF01F2E7DAC26>I<1306A5130E A4131EA3133E137EA213FE12011207001FB512F0B6FCA2C648C7FCB3A4150CAA017E131C 017F1318A26D133890381F8030ECC070903807E0E0903801FFC09038007F001E3E7EBC26 >III< B539F001FFFCA3000790C7EA7FE06C48EC1F8000011600160E0000150C6D141C6D1418A2 6E1338013F1430A26D6C5BA26E13E0010F5CA26D6C485AA2ECF803010391C7FCA2903801 FC06A2ECFE0E0100130CA2EC7F18A215B8EC3FB0A2EC1FE0A36E5AA26E5AA36EC8FCA214 06A35CA25CA2123C007E5BB4FC5CA25CEAFE01387C0380D87007C9FCEA3C1EEA0FFCEA03 F02E3F7EAA33>121 D<003FB612E0A29038C0003F90C713C0003CEC7F800038ECFF00A2 0030495A0070495AA24A5A0060495AA24A5A4A5AA2C7485A4AC7FC5B5C495A13075C495A 131F4A1360495A495AA249C712C0485AA2485A485A1501485A48481303A24848EB078048 48131F00FF14FF90B6FCA2232B7DAA2B>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FA cmbx12 17.28 27 /FA 27 122 df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ndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%BeginPaperSize: a4 a4 %%EndPaperSize %%EndSetup %%Page: 1 1 1 0 bop 290 409 a FA(Quan)l(tum)52 b(Mec)l(hanics)h(of)h(Damp)t(ed)f (Systems)e(I)t(I.)368 591 y(Damping)i(and)h(P)l(arab)t(olic)i(P)l(oten) l(tial)d(Barrier.)1427 844 y Fz(Dariusz)32 b(Chru)-5 b(\023)-44 b(sci)s(\023)-51 b(nski)742 960 y(Institute)33 b(of)f(Ph)m(ysics,)j(Nicolaus)c(Cop)s(ernicus)i(Univ)m(ersit)m(y)931 1076 y(ul.)42 b(Grudzi)s(\030)-46 b(adzk)-5 b(a)32 b(5/7,)g(87-100)f(T) -8 b(oru)s(\023)-51 b(n,)32 b(P)m(oland)1672 1412 y Fy(Abstract)375 1563 y Fx(W)-7 b(e)33 b(in)n(v)n(estigate)d(the)j(resonan)n(t)d(states) i(for)f(the)i(parab)r(olic)d(p)r(oten)n(tial)i(barrier)e(kno)n(wn)i (also)f(as)251 1662 y(in)n(v)n(erted)20 b(or)g(rev)n(ersed)f (oscillator.)33 b(They)21 b(corresp)r(ond)e(to)i(the)g(p)r(oles)f(of)h (meromorphic)f(con)n(tin)n(uation)251 1762 y(of)31 b(the)g(resolv)n(en) n(t)e(op)r(erator)h(to)g(the)i(complex)e(energy)g(plane.)47 b(As)31 b(a)f(b)n(ypro)r(duct)h(w)n(e)g(establish)f(an)251 1862 y(in)n(teresting)d(relation)g(b)r(et)n(w)n(een)h(parab)r(olic)f (cylinder)g(functions)i(\(represen)n(ting)d(energy)h(eigenfunc-)251 1961 y(tions)g(of)h(our)f(system\))g(and)h(a)f(class)g(of)g(Gel'fand)h (distributions)g(used)f(in)h(our)f(recen)n(t)g(pap)r(er.)24 2314 y Fw(Mathematical)33 b(Sub)6 b(ject)35 b(Classi\014cations)g (\(2000\):)41 b Fv(46E10,)32 b(46F05,)h(46N50,)g(47A10.)24 2498 y Fw(Key)i(w)m(ords:)40 b Fv(quan)m(tum)30 b(mec)m(hanics,)h (distributions,)26 b(sp)s(ectral)k(theorem,)h(Gel'fand)f(triplets.)24 2784 y Fu(1)134 b(In)l(tro)t(duction)24 2987 y Fv(In)29 b(a)i(recen)m(t)g(pap)s(er)f([1])h(w)m(e)g(ha)m(v)m(e)g(in)m(v)m (estigated)h(a)e(quan)m(tization)h(of)f(the)h(simple)d(damp)s(ed)h (system)3473 2954 y Ft(1)1668 3190 y Fv(_)-41 b Fs(u)26 b Fv(=)f Fr(\000)p Fs(\015)5 b(u)30 b(:)1442 b Fv(\(1.1\))24 3393 y(T)-8 b(o)28 b(quan)m(tize)g(this)f(system)h(w)m(e)g(double)e (the)i(n)m(um)m(b)s(er)f(of)h(degrees)g(of)g(freedom,)h(i.e.)39 b(together)30 b(with)c(\(1.1\))24 3506 y(w)m(e)32 b(consider)45 b(_)-39 b Fs(v)32 b Fv(=)c(+)p Fs(\015)5 b(v)s Fv(.)46 b(The)32 b(enlarged)g(system)g(is)g(a)g(Hamiltonian)f(one)h(and)g(its)f (quan)m(tization)i(leads)24 3619 y(to)e(the)f(follo)m(wing)f(quan)m (tum)h(Hamiltonian:)1484 3813 y Fq(b)1463 3836 y Fs(H)i Fv(=)25 b Fr(\000)1748 3775 y Fs(\015)p 1748 3815 53 4 v 1751 3899 a Fv(2)1810 3836 y(\()s Fq(b)-54 b Fs(u)q Fq(b)i Fs(v)24 b Fv(+)d Fq(b)-52 b Fs(v)6 b Fq(b)-54 b Fs(u)p Fv(\))31 b Fs(:)1252 b Fv(\(1.2\))24 4070 y(W)-8 b(e)29 b(sho)m(w)m(ed)g(that)h(the)f(ab)s(o)m(v)m(e)g(system)g(displa)m (ys)e(t)m(w)m(o)j(families)d(of)h(generalized)h(eigen)m(v)m(ectors)h Fs(f)3370 4037 y Fp(\006)3360 4093 y Fo(n)3457 4070 y Fv(corre-)24 4183 y(sp)s(onding)21 b(to)j(purely)e(imaginary)g(eigen)m (v)-5 b(alues)1687 4160 y Fq(b)1666 4183 y Fs(H)7 b(f)1804 4150 y Fp(\006)1794 4206 y Fo(n)1887 4183 y Fv(=)25 b Fr(\006)p Fs(E)2121 4197 y Fo(n)2168 4183 y Fs(f)2223 4150 y Fp(\006)2213 4206 y Fo(n)2281 4183 y Fv(.)39 b(These)23 b(eigen)m(v)m(ectors)j(are)e(in)m(terpreted)24 4296 y(as)g(resonan)m(t) h(states)h(|)e(they)h(corresp)s(ond)e(to)i(the)g(p)s(oles)e(of)i (energy)g(eigenfunctions)e(when)g(con)m(tin)m(ued)h(to)24 4409 y(the)f(complex)g(energy)h(plane.)38 b(It)23 b(turns)g(out)g(that) h(resonan)m(t)g(states)h(are)f(resp)s(onsible)d(for)i(the)g(irrev)m (ersible)24 4522 y(b)s(eha)m(vior.)49 b(W)-8 b(e)35 b(sho)m(w)m(ed)f (that)g(there)g(are)g(t)m(w)m(o)h(dense)e(subspaces)g(\010)2419 4536 y Fp(\006)2509 4522 y Fr(2)d Fs(L)2662 4489 y Ft(2)2701 4522 y Fv(\()p Fn(R)s Fv(\))40 b(suc)m(h)34 b(that)g(restriction)24 4651 y(of)c(the)h(unitary)f(group)g Fs(U)10 b Fv(\()p Fs(t)p Fv(\))26 b(=)f Fs(e)1203 4618 y Fp(\000)p Fo(i)1298 4601 y Fm(b)1282 4618 y Fo(H)6 b(t)1406 4651 y Fv(to)31 b(\010)1583 4665 y Fp(\006)1672 4651 y Fv(do)s(es)g(no)f(longer)h (de\014ne)e(a)i(group)g(but)f(giv)m(es)h(rise)e(to)j(t)m(w)m(o)24 4764 y(semigroups:)49 b Fs(U)602 4778 y Fp(\000)661 4764 y Fv(\()p Fs(t)p Fv(\))34 b(=)f Fs(U)10 b Fv(\()p Fs(t)p Fv(\))p Fr(j)1102 4778 y Ft(\010)1153 4787 y Fl(\000)1245 4764 y Fv(de\014ned)34 b(for)h Fs(t)e Fr(\025)g Fv(0)j(and)f Fs(U)2202 4778 y Ft(+)2261 4764 y Fv(\()p Fs(t)p Fv(\))f(=)f Fs(U)10 b Fv(\()p Fs(t)p Fv(\))p Fr(j)2702 4778 y Ft(\010)2753 4787 y Fk(+)2844 4764 y Fv(de\014ned)34 b(for)h Fs(t)e Fr(\024)g Fv(0.)56 b(In)p 24 4855 1465 4 v 127 4909 a Fk(1)162 4940 y Fj(W)-6 b(e)30 b(sligh)n(tly)g(c)n(hange)h(the)e (notation:)44 b(the)30 b(co)r(ordinates)h(\()p Fi(x;)13 b(p)p Fj(\))29 b(used)h(in)g([1)q(])g(are)h(replaced)f(b)n(y)g(\()p Fi(u;)13 b(v)s Fj(\))30 b(in)g(the)f(presen)n(t)24 5032 y(pap)r(er.)1832 5281 y Fv(1)p eop %%Page: 2 2 2 1 bop 24 44 a Fv(the)36 b(framew)m(ork)h(of)g(Gel'fand)f(triplets)f (\(see)j(e.g.)61 b([2]\))38 b(it)e(means)g(that)i(the)f(quan)m(tum)f(v) m(ersion)g(of)h(the)24 157 y(damp)s(ed)29 b(system)h(\(1.1\))i(corresp) s(onds)d(to)i(the)g(Gel'fand)f(triplet:)1432 353 y(\010)1498 367 y Fp(\000)1597 353 y Fr(\032)40 b Fs(L)1770 315 y Ft(2)1809 353 y Fv(\()p Fn(R)s Fv(\))47 b Fr(\032)40 b Fv(\010)2163 315 y Fp(0)2163 375 y(\000)2252 353 y Fs(;)1221 b Fv(\(1.3\))24 561 y(together)29 b(with)d(the)i(Hamiltonian) 1280 538 y Fq(b)1259 561 y Fs(H)6 b Fr(j)1366 575 y Ft(\010)1417 584 y Fl(\000)1474 561 y Fv(.)40 b(This)26 b(system)i(serv)m(es)g(as)g (a)g(simple)e(example)h(of)h(Arno)g(Bohm)24 674 y(theory)i(of)h (resonances)g([3])g(\(see)g(also)f([4)q(,)h(5]\))g(and)f(illustrates)e (mathematical)j(results)e(of)i([6].)165 787 y(In)i(the)g(presen)m(t)h (pap)s(er)e(w)m(e)i(con)m(tin)m(ue)g(to)g(study)f(this)f(system)i(but)f (in)f(a)i(di\013eren)m(t)f(represen)m(tation.)24 900 y(Let)e(us)e(observ)m(e)i(that)g(p)s(erforming)d(the)j(linear)e (canonical)h(transformation)f(\()p Fs(u;)15 b(v)s Fv(\))27 b Fr(\000)-15 b(!)25 b Fv(\()p Fs(x;)15 b(p)p Fv(\):)1264 1128 y Fs(u)25 b Fv(=)1447 1067 y Fs(\015)5 b(x)20 b Fr(\000)g Fs(p)p 1447 1107 261 4 v 1491 1125 a Fr(p)p 1566 1125 98 4 v 1566 1192 a Fv(2)p Fs(\015)1748 1128 y(;)167 b(v)29 b Fv(=)2119 1067 y Fs(\015)5 b(x)20 b Fv(+)g Fs(p)p 2119 1107 261 4 v 2162 1125 a Fr(p)p 2238 1125 98 4 v 67 x Fv(2)p Fs(\015)2420 1128 y(;)1053 b Fv(\(1.4\))24 1367 y(one)30 b(obtains)g(for)g(the)h(Hamiltonian)1488 1555 y Fq(b)1467 1578 y Fs(H)h Fv(=)1681 1516 y(1)p 1681 1557 46 4 v 1681 1640 a(2)1736 1578 y(\()5 b Fq(b)-56 b Fs(p)1817 1540 y Ft(2)1877 1578 y Fr(\000)20 b Fs(\015)2020 1540 y Ft(2)2063 1578 y Fq(b)-54 b Fs(x)2112 1540 y Ft(2)2151 1578 y Fv(\))31 b Fs(:)1256 b Fv(\(1.5\))24 1807 y(It)33 b(represen)m(ts)h(the)g(parab)s(olic)e(p)s(oten)m(tial)h(barrier)f Fs(V)20 b Fv(\()p Fs(x)p Fv(\))32 b(=)e Fr(\000)p Fs(\015)2257 1774 y Ft(2)2297 1807 y Fs(x)2349 1774 y Ft(2)2388 1807 y Fs(=)p Fv(2)35 b(and)e(it)g(w)m(as)h(studied)e(b)m(y)i(sev)m(eral)24 1919 y(authors)f(in)g(v)-5 b(arious)33 b(con)m(texts)j([7)q(,)e(8)q(,)g (9)q(,)g(10)q(,)g(11)q(,)h(12)q(,)f(13)q(].)52 b(It)34 b(is)g(w)m(ell)f(kno)m(wn)g(that)i(this)e(system)i(giv)m(es)24 2032 y(rise)g(to)i(the)f(generalized)g(complex)g(eigen)m(v)-5 b(alues)36 b(|)g(the)h(ph)m(ysical)d(reason)j(for)f(that)h(is)e(the)i (p)s(oten)m(tial)24 2145 y(un)m(b)s(ounded)d(from)i(b)s(elo)m(w.)60 b(W)-8 b(e)38 b(\014nd)e(the)h(corresp)s(onding)e(energy)i(eigenstates) h(for)f(\(1.5\).)62 b(They)37 b(are)24 2258 y(giv)m(en)h(in)g(terms)g (of)h(parab)s(olic)e(cylinder)g(functions)g Fs(D)1992 2272 y Fo(\027)2035 2258 y Fv(\()p Fs(x)p Fv(\).)67 b(Using)38 b(the)h(Gel'fand-Maurin)e(sp)s(ectral)24 2371 y(decomp)s(osition)e(w)m (e)j(\014nd)e(the)h(resolv)m(en)m(t)h(op)s(erator)g Fs(R)q Fv(\()p Fs(z)t(;)2098 2348 y Fq(b)2076 2371 y Fs(H)7 b Fv(\))37 b(=)g(\()2395 2348 y Fq(b)2374 2371 y Fs(H)32 b Fr(\000)24 b Fs(z)t Fv(\))2658 2338 y Fp(\000)p Ft(1)2790 2371 y Fv(and)37 b(relate)g(its)g(p)s(oles)f(to)24 2484 y(the)j(resonan)m(t)h(states.)68 b(As)39 b(a)h(b)m(ypro)s(duct)e(w)m(e) h(established)f(a)h(deep)g(relation)f(b)s(et)m(w)m(een)i(the)g (Gel'fand)24 2597 y(distributions)22 b Fs(u)603 2564 y Fo(\025)603 2619 y Fp(\006)688 2597 y Fv([14)q(,)27 b(15)q(])f(\(used)g(in)f([1)q(]\))h(and)g(parab)s(olic)e(cylinder)g (functions)h Fs(D)2866 2611 y Fo(\027)2910 2597 y Fv(\()p Fs(x)p Fv(\).)40 b(The)25 b(details)h(are)24 2710 y(included)h(in)i (the)i(App)s(endix.)24 2995 y Fu(2)134 b(In)l(v)l(erted)46 b(oscillator)h(and)e(complex)g(eigen)l(v)-7 b(alues)24 3198 y Fv(Let)26 b(us)e(note)i(that)703 3175 y Fq(b)682 3198 y Fs(H)32 b Fv(de\014ned)25 b(in)f(\(1.5\))j(corresp)s(onds)d(to)i (the)g(Hamiltonian)d(of)j(the)f(harmonic)g(oscillator)24 3311 y(with)34 b(purely)g(imaginary)g(frequency)h Fs(!)i Fv(=)d Fr(\006)p Fs(i\015)40 b Fv(\(in)35 b(the)h(literature)f(it)g(is) g(also)g(called)g(an)g(in)m(v)m(erted)h(or)24 3424 y(rev)m(ersed)h (oscillator\).)61 b(The)36 b(connection)h(with)f(a)i(harmonic)e (oscillator)g(ma)m(y)i(b)s(e)e(established)g(b)m(y)h(the)24 3537 y(follo)m(wing)28 b(scaling)i(op)s(erator)h([16)q(]:)1339 3759 y Fq(b)1328 3782 y Fs(V)1381 3797 y Fo(\025)1451 3782 y Fv(:=)25 b(exp)1726 3654 y Fq(\022)1803 3720 y Fs(\025)p 1803 3761 54 4 v 1807 3844 a Fv(2)1866 3782 y(\()s Fq(b)-54 b Fs(x)6 b Fq(b)-56 b Fs(p)20 b Fv(+)25 b Fq(b)-57 b Fs(p)s Fq(b)j Fs(x)p Fv(\))2243 3654 y Fq(\023)2356 3782 y Fs(;)1117 b Fv(\(2.1\))24 4027 y(with)27 b Fs(\025)e Fr(2)g Fn(R)s Fv(.)46 b(Using)28 b(comm)m(utation)h(relation)f([)s Fq(b)-54 b Fs(x;)21 b Fq(b)-57 b Fs(p)p Fv(])26 b(=)f Fs(i)p Fv(,)k(this)f(op)s(erator)h(ma)m(y)g(b)s(e)f(rewritten)g(as)h (follo)m(ws)1248 4217 y Fq(b)1236 4240 y Fs(V)1289 4255 y Fo(\025)1360 4240 y Fv(=)c Fs(e)1498 4203 y Fp(\000)p Fo(i)1587 4175 y Fh(\025)p 1587 4187 37 3 v 1590 4229 a Fk(2)1653 4240 y Fs(e)1695 4203 y Fo(\025)r Fm(b)-41 b Fo(x)t Fm(b)e Fo(p)1841 4240 y Fv(=)25 b Fs(e)1979 4203 y Fp(\000)p Fo(i)2068 4175 y Fh(\025)p 2068 4187 V 2071 4229 a Fk(2)2134 4240 y Fs(e)2176 4203 y Fp(\000)p Fo(i\025x@)2373 4211 y Fh(x)2447 4240 y Fs(;)1026 b Fv(\(2.2\))24 4436 y(and)34 b(therefore)h(it)f(de\014nes)g(a)h(complex)f(dilation,)g (i.e.)54 b(the)34 b(action)h(of)2520 4413 y Fq(b)2508 4436 y Fs(V)2561 4451 y Fo(\025)2641 4436 y Fv(on)g(a)g(function)e Fs(')g Fv(=)f Fs(')p Fv(\()p Fs(x)p Fv(\))k(is)24 4548 y(giv)m(en)30 b(b)m(y)1349 4651 y Fq(b)1338 4674 y Fs(V)1391 4689 y Fo(\025)1451 4674 y Fs(')p Fv(\()p Fs(x)p Fv(\))d(=)d Fs(e)1796 4636 y Fp(\000)p Fo(i)1885 4609 y Fh(\025)p 1886 4621 V 1889 4662 a Fk(2)1952 4674 y Fs(')p Fv(\()p Fs(e)2088 4636 y Fp(\000)p Fo(i\025)2228 4674 y Fs(x)p Fv(\))31 b Fs(:)1127 b Fv(\(2.3\))24 4836 y(In)29 b(particular)g(one)i (easily)e(\014nds:)1030 5009 y Fq(b)1019 5032 y Fs(V)1072 5047 y Fo(\025)1136 5032 y Fq(b)-55 b Fs(x)1211 5009 y Fq(b)1199 5032 y Fs(V)1273 4993 y Fp(\000)p Ft(1)1252 5061 y Fo(\025)1392 5032 y Fv(=)25 b Fs(e)1530 4994 y Fp(\000)p Fo(i\025)1658 5032 y Fq(b)-54 b Fs(x)30 b(;)2025 5009 y Fq(b)2014 5032 y Fs(V)2067 5047 y Fo(\025)2132 5032 y Fq(b)-56 b Fs(p)2199 5009 y Fq(b)2188 5032 y Fs(V)2261 4993 y Fp(\000)p Ft(1)2241 5061 y Fo(\025)2381 5032 y Fv(=)25 b Fs(e)2519 4994 y Fo(i\025)2594 5032 y Fq(b)-56 b Fs(p)30 b(;)808 b Fv(\(2.4\))1832 5281 y(2)p eop %%Page: 3 3 3 2 bop 24 44 a Fv(and)29 b(hence)997 134 y Fq(b)986 157 y Fs(V)1039 172 y Fo(\025)1099 157 y Fv(\()5 b Fq(b)-56 b Fs(p)1180 120 y Ft(2)1240 157 y Fr(\000)20 b Fs(\015)1383 120 y Ft(2)1426 157 y Fq(b)-54 b Fs(x)1475 120 y Ft(2)1514 157 y Fv(\))1576 134 y Fq(b)1564 157 y Fs(V)1638 119 y Fp(\000)p Ft(1)1617 186 y Fo(\025)1757 157 y Fv(=)25 b Fs(e)1895 120 y Ft(2)p Fo(i\025)2015 157 y Fv(\()5 b Fq(b)-56 b Fs(p)2096 120 y Ft(2)2156 157 y Fr(\000)20 b Fs(e)2289 120 y Fp(\000)p Ft(4)p Fo(i\025)2449 157 y Fs(\015)2501 120 y Ft(2)2544 157 y Fq(b)-55 b Fs(x)2592 120 y Ft(2)2632 157 y Fv(\))30 b Fs(:)776 b Fv(\(2.5\))24 324 y(Therefore,)30 b(for)g Fs(e)642 291 y Ft(4)p Fo(i\025)772 324 y Fv(=)25 b Fr(\000)p Fv(1,)31 b(i.e.)41 b Fs(\025)25 b Fv(=)g Fr(\006)p Fs(\031)s(=)p Fv(4,)31 b(one)g(has)1367 505 y Fq(b)1356 528 y Fs(V)1409 547 y Fp(\006)p Fo(\031)r(=)p Ft(4)1618 505 y Fq(b)1596 528 y Fs(H)1706 505 y Fq(b)1694 528 y Fs(V)1768 490 y Fp(\000)p Ft(1)1747 561 y Fp(\006)p Fo(\031)r(=)p Ft(4)1945 528 y Fv(=)25 b Fr(\006)p Fs(i)2165 505 y Fq(b)2143 528 y Fs(H)2219 543 y Ft(ho)2328 528 y Fs(;)1145 b Fv(\(2.6\))24 732 y(where)1452 838 y Fq(b)1431 861 y Fs(H)1507 876 y Ft(ho)1611 861 y Fv(=)1717 799 y(1)p 1717 840 46 4 v 1717 923 a(2)1772 861 y(\()5 b Fq(b)-56 b Fs(p)1853 823 y Ft(2)1913 861 y Fv(+)20 b Fs(\015)2056 823 y Ft(2)2098 861 y Fq(b)-54 b Fs(x)2147 823 y Ft(2)2187 861 y Fv(\))30 b Fs(;)1221 b Fv(\(2.7\))24 1065 y(stands)23 b(for)g(the)h(oscillator)f(Hamiltonian.)37 b(In)23 b(particular)f(if)g Fs(E)2190 1032 y Ft(ho)2185 1087 y Fo(n)2295 1065 y Fv(=)j Fs(\015)5 b Fv(\()p Fs(n)i Fv(+)2627 1029 y Ft(1)p 2627 1044 36 4 v 2627 1096 a(2)2672 1065 y Fv(\))24 b(is)f(an)g(oscillator)g(sp)s(ectrum)1494 1261 y Fq(b)1472 1284 y Fs(H)1548 1299 y Ft(ho)1626 1284 y Fs( )1688 1247 y Ft(ho)1685 1307 y Fo(n)1793 1284 y Fv(=)i Fs(E)1961 1247 y Ft(ho)1956 1307 y Fo(n)2040 1284 y Fs( )2102 1247 y Ft(ho)2099 1307 y Fo(n)2211 1284 y Fs(;)1262 b Fv(\(2.8\))24 1488 y(then)1565 1578 y Fq(b)1543 1601 y Fs(H)7 b Fg(f)1656 1564 y Fp(\006)1656 1624 y Fo(n)1740 1601 y Fv(=)25 b Fr(\006)p Fs(E)1974 1615 y Fo(n)2021 1601 y Fg(f)2051 1564 y Fp(\006)2051 1624 y Fo(n)2140 1601 y Fs(;)1333 b Fv(\(2.9\))24 1768 y(with)1318 1908 y Fs(E)1385 1922 y Fo(n)1457 1908 y Fv(=)25 b Fs(iE)1656 1871 y Ft(ho)1651 1931 y Fo(n)1761 1908 y Fv(=)g Fs(i\015)1955 1780 y Fq(\022)2022 1908 y Fs(n)20 b Fv(+)2198 1847 y(1)p 2198 1887 46 4 v 2198 1971 a(2)2253 1780 y Fq(\023)2366 1908 y Fs(;)1062 b Fv(\(2.10\))24 2120 y(and)1025 2233 y Fg(f)1055 2195 y Fp(\006)1055 2255 y Fo(n)1113 2233 y Fv(\()p Fs(x)p Fv(\))26 b(=)1369 2210 y Fq(b)1357 2233 y Fs(V)1410 2251 y Fp(\007)p Fo(\031)r(=)p Ft(4)1598 2233 y Fs( )1660 2195 y Ft(ho)1657 2255 y Fo(n)1739 2233 y Fv(\()p Fs(x)p Fv(\))g(=)f Fs(e)2025 2195 y Fp(\006)p Fo(i)2114 2168 y Fh(\031)p 2114 2180 38 3 v 2118 2221 a Fk(8)2181 2233 y Fs( )2243 2195 y Ft(ho)2240 2255 y Fo(n)2322 2233 y Fv(\()p Fs(e)2399 2195 y Fp(\006)p Fo(i)2488 2168 y Fh(\031)p 2489 2180 V 2493 2221 a Fk(4)2541 2233 y Fs(x)p Fv(\))31 b Fs(:)769 b Fv(\(2.11\))24 2400 y(No)m(w,)31 b(recalling)e(that)i(\(see)g(e.g.)42 b([17)q(]\))1264 2615 y Fs( )1326 2578 y Ft(ho)1323 2638 y Fo(n)1405 2615 y Fv(\()p Fs(x)p Fv(\))26 b(=)f Fs(N)1722 2629 y Fo(n)1784 2615 y Fs(e)1826 2578 y Fp(\000)1891 2547 y Fh(\015)p 1892 2563 36 3 v 1895 2604 a Fk(2)1937 2578 y Fo(x)1977 2554 y Fk(2)2016 2615 y Fs(H)2092 2629 y Fo(n)2138 2615 y Fv(\()2173 2554 y Fr(p)p 2249 2554 53 4 v 61 x Fs(\015)6 b(x)p Fv(\))30 b Fs(;)1009 b Fv(\(2.12\))24 2820 y(where)30 b Fs(H)363 2834 y Fo(n)439 2820 y Fv(stands)g(for)g(the)h(n-th)f (Hermite)g(p)s(olynomial)e(and)i(the)g(normalization)f(constan)m(t)1443 3102 y Fs(N)1516 3116 y Fo(n)1588 3102 y Fv(=)1684 2973 y Fq(\022)1848 2979 y Fr(p)p 1924 2979 V 57 x Fs(\015)p 1761 3081 304 4 v 1761 3164 a Fv(2)1806 3138 y Fo(n)1853 3164 y Fs(n)p Fv(!)1933 3099 y Fr(p)p 2009 3099 56 4 v 65 x Fs(\031)2074 2973 y Fq(\023)2151 2969 y Fk(1)p 2151 2981 31 3 v 2151 3022 a(2)2241 3102 y Fs(;)1187 b Fv(\(2.13\))24 3376 y(one)30 b(obtains)g(the)h(follo)m(wing)d(form)m (ulae)i(for)h(the)f(generalized)g(eigen)m(v)m(ectors)i(of)2822 3353 y Fq(b)2801 3376 y Fs(H)7 b Fv(:)1209 3580 y Fg(f)1239 3543 y Fp(\006)1239 3603 y Fo(n)1298 3580 y Fv(\()p Fs(x)p Fv(\))26 b(=)e Fs(N)1624 3543 y Fp(\006)1614 3603 y Fo(n)1699 3580 y Fs(e)1741 3543 y Fp(\007)p Fo(i)1830 3512 y Fh(\015)p 1830 3528 36 3 v 1833 3569 a Fk(2)1875 3543 y Fo(x)1915 3519 y Fk(2)1954 3580 y Fs(H)2030 3594 y Fo(n)2076 3580 y Fv(\()2111 3500 y Fq(p)p 2203 3500 155 4 v 2203 3580 a Fr(\006)p Fs(i\015)5 b(x)p Fv(\))31 b Fs(;)953 b Fv(\(2.14\))24 3785 y(with)1212 3962 y Fs(N)1295 3924 y Fp(\006)1285 3984 y Fo(n)1379 3962 y Fv(=)25 b Fs(e)1517 3924 y Fp(\006)p Fo(i)1606 3897 y Fh(\031)p 1606 3909 38 3 v 1610 3950 a Fk(8)1674 3962 y Fs(N)1747 3976 y Fo(n)1819 3962 y Fv(=)1915 3834 y Fq(\022)2028 3833 y Fr(p)p 2104 3833 155 4 v 67 x(\006)p Fs(i\015)p 1992 3941 304 4 v 1992 4025 a Fv(2)2037 3998 y Fo(n)2084 4025 y Fs(n)p Fv(!)2164 3959 y Fr(p)p 2240 3959 56 4 v 66 x Fs(\031)2305 3834 y Fq(\023)2382 3825 y Fk(1)p 2382 3837 31 3 v 2382 3878 a(2)2472 3962 y Fs(:)956 b Fv(\(2.15\))24 4186 y(Clearly)-8 b(,)26 b Fg(f)384 4153 y Fp(\006)384 4209 y Fo(n)468 4186 y Fv(are)g(not)g(elemen)m(ts)h(from)e Fs(L)1412 4153 y Ft(2)1451 4186 y Fv(\()p Fn(R)s Fv(\))32 b(but)26 b(they)g(do)f(b)s(elong)g(to)i(the)f(dual)e(of)i(the)g(Sc)m(h)m(w)m (artz)h(space)24 4299 y Fr(S)7 b Fv(\()p Fn(R)181 4313 y Fo(x)230 4299 y Fv(\))265 4266 y Fp(0)289 4299 y Fv(,)31 b(i.e.)40 b(they)31 b(are)f(temp)s(ered)g(distributions.)24 4512 y Fw(Prop)s(osition)36 b(1)46 b Ff(Two)33 b(families)g(of)g(gener) -5 b(alize)g(d)34 b(eigenve)-5 b(ctors)33 b Fg(f)2338 4479 y Fp(\006)2338 4534 y Fo(n)2429 4512 y Ff(satisfy)h(the)f(fol)5 b(lowing)33 b(pr)-5 b(op)g(erties:)131 4699 y(1.)46 b(they)33 b(ar)-5 b(e)34 b(c)-5 b(onjugate)g(d)34 b(to)f(e)-5 b(ach)33 b(other:)p 1667 4824 212 4 v 1667 4913 a Fg(f)1697 4875 y Ft(+)1697 4925 y Fo(n)1756 4913 y Fv(\()p Fs(x)p Fv(\))26 b(=)f Fg(f)2030 4876 y Fp(\000)2030 4936 y Fo(n)2088 4913 y Fv(\()p Fs(x)p Fv(\))34 b Fs(;)1184 b Fv(\(2.16\))1832 5281 y(3)p eop %%Page: 4 4 4 3 bop 131 44 a Ff(2.)46 b(they)33 b(ar)-5 b(e)34 b(orthonormal)1648 157 y Fr(h)15 b Fg(f)1728 120 y Fp(\006)1728 180 y Fo(n)1787 157 y Fr(j)p Fg(f)1842 120 y Fp(\007)1842 180 y Fo(m)1924 157 y Fr(i)25 b Fv(=)g Fs(\016)2120 171 y Fo(nm)2263 157 y Fs(;)1165 b Fv(\(2.17\))131 340 y Ff(3.)46 b(they)33 b(ar)-5 b(e)34 b(c)-5 b(omplete)1429 404 y Fp(1)1398 431 y Fq(X)1397 626 y Fo(n)p Ft(=0)p 1546 429 212 4 v 1546 518 a Fg(f)1576 480 y Fp(\006)1576 530 y Fo(n)1634 518 y Fv(\()p Fs(x)p Fv(\))16 b Fg(f)1802 480 y Fp(\007)1802 540 y Fo(n)1861 518 y Fv(\()p Fs(x)1948 480 y Fp(0)1971 518 y Fv(\))26 b(=)f Fs(\016)s Fv(\()p Fs(x)c Fr(\000)f Fs(x)2422 480 y Fp(0)2445 518 y Fv(\))33 b Fs(:)915 b Fv(\(2.18\))24 775 y(The)30 b(pro)s(of)f(follo)m(ws)h(immediately)f (from)h(orthonormalit)m(y)g(and)g(completness)g(of)h(oscillator)f (eigenfunc-)24 888 y(tions)k Fs( )313 855 y Ft(ho)310 910 y Fo(n)392 888 y Fv(.)54 b(F)-8 b(orm)m(ula)35 b(\(2.16\))i (implies)32 b(that)k Fg(f)1645 855 y Ft(+)1645 910 y Fo(n)1738 888 y Fv(and)e Fg(f)1949 855 y Fp(\000)1949 910 y Fo(n)2043 888 y Fv(are)h(related)g(b)m(y)f(the)h(time)g(rev)m (ersal)g(op)s(erator)24 1000 y Fw(T)p Fv(:)51 b Fw(T)p Fs( )38 b Fv(:=)p 474 926 63 4 v 35 w Fs( )s Fv(.)57 b(Recall)36 b([1)q(])g(that)h(in)d Fs(u)p Fv(-represen)m(tation)j Fw(T)e Fv(is)g(unitary)g(\(it)h(is)f(de\014ned)f(b)m(y)i(the)g(F)-8 b(ourier)24 1113 y(transformation\),)30 b(whereas)g(in)f Fs(x)p Fv(-represen)m(tation)i(it)f(is)f(an)m(tiunitary)-8 b(.)24 1395 y Fu(3)134 b(Change)46 b(of)f(represen)l(tation)24 1598 y Fv(It)25 b(should)f(b)s(e)g(clear)i(that)g(there)f(exists)g (relation)g(b)s(et)m(w)m(een)h(generalized)f(eigen)m(v)m(ectors)i Fg(f)3070 1565 y Fp(\006)3070 1620 y Fo(n)3129 1598 y Fv(\()p Fs(x)p Fv(\))f(and)f Fs(f)3504 1565 y Fp(\006)3494 1620 y Fo(n)3562 1598 y Fv(\()p Fs(u)p Fv(\))24 1711 y(found)k(in)g([1]:)1102 1824 y Fs(f)1157 1786 y Ft(+)1147 1846 y Fo(n)1215 1824 y Fv(\()p Fs(u)p Fv(\))41 b Fr(\030)f Fs(u)1541 1786 y Fo(n)1619 1824 y Fs(;)251 b(f)1950 1786 y Fp(\000)1940 1846 y Fo(n)2009 1824 y Fv(\()p Fs(u)p Fv(\))41 b Fr(\030)f Fs(\016)2326 1786 y Ft(\()p Fo(n)p Ft(\))2429 1824 y Fv(\()p Fs(u)p Fv(\))31 b Fs(:)891 b Fv(\(3.1\))24 1975 y(They)29 b(de\014ne)h(the)h(same)f(eigen)m(v)m (ectors)48 b Fr(j)20 b(\006)g Fs(n)15 b Fr(i)46 b Fv(but)29 b(in)h(di\013eren)m(t)f(represen)m(tations:)984 2148 y Fg(f)1014 2110 y Fp(\006)1014 2170 y Fo(n)1073 2148 y Fv(\()p Fs(x)p Fv(\))d(=)f Fr(h)15 b Fs(x)p Fr(j)21 b(\006)f Fs(n)15 b Fr(i)30 b Fs(;)252 b(f)2023 2110 y Fp(\006)2013 2170 y Fo(n)2081 2148 y Fv(\()p Fs(u)p Fv(\))26 b(=)f Fr(h)15 b Fs(u)p Fr(j)21 b(\006)f Fs(n)15 b Fr(i)30 b Fs(:)24 2321 y Fv(T)-8 b(o)36 b(\014nd)e(this)g(relation)h(let)g(us)g (observ)m(e)h(that)g(the)g(canonical)f(transformation)g(\(1.4\))i(is)e (generated)h(b)m(y)24 2434 y(the)30 b(follo)m(wing)f(generating)i (function)1210 2640 y Fs(S)5 b Fv(\()p Fs(x;)15 b(u)p Fv(\))27 b(=)1618 2578 y Fs(\015)p 1618 2619 53 4 v 1621 2702 a Fv(2)1680 2640 y Fs(x)1732 2602 y Ft(2)1791 2640 y Fr(\000)1882 2560 y Fq(p)p 1973 2560 98 4 v 80 x Fv(2)p Fs(\015)6 b(xu)20 b Fv(+)2296 2578 y(1)p 2296 2619 46 4 v 2296 2702 a(2)2351 2640 y Fs(u)2403 2602 y Ft(2)2473 2640 y Fs(;)1000 b Fv(\(3.2\))24 2834 y(that)31 b(is,)1336 2984 y Fs(p)25 b Fv(=)1513 2923 y Fs(@)5 b(S)p 1513 2964 115 4 v 1518 3047 a(@)g(x)1667 2984 y(;)252 b(v)28 b Fv(=)d Fr(\000)2193 2923 y Fs(@)5 b(S)p 2193 2964 V 2197 3047 a(@)g(u)2348 2984 y(:)1125 b Fv(\(3.3\))24 3157 y(Let)31 b(us)e(de\014ne)h(a)h(unitary)e(op)s(erator)1315 3330 y Fr(U)64 b Fv(:)56 b Fs(L)1579 3292 y Ft(2)1618 3330 y Fv(\()p Fn(R)1713 3344 y Fo(u)1764 3330 y Fv(\))g Fr(\000)-15 b(!)55 b Fs(L)2119 3292 y Ft(2)2158 3330 y Fv(\()p Fn(R)2253 3344 y Fo(x)2303 3330 y Fv(\))31 b Fs(;)24 3503 y Fv(b)m(y)962 3655 y Fs(f)126 b Fr(\000)-16 b(!)116 b Fv(\()p Fr(U)9 b Fs(f)h Fv(\)\()p Fs(x)p Fv(\))26 b(=)f Fs(C)1932 3531 y Fq(Z)2023 3557 y Fp(1)1982 3737 y(\0001)2127 3655 y Fs(f)10 b Fv(\()p Fs(u)p Fv(\))p Fs(e)2346 3617 y Fo(iS)t Ft(\()p Fo(x;u)p Ft(\))2592 3655 y Fs(du)30 b(;)752 b Fv(\(3.4\))24 3854 y(where)30 b(the)g(constan)m(t)i(`)p Fs(C)7 b Fv(')30 b(is)f(determined)g(b)m(y) 1020 4066 y Fr(j)p Fs(C)7 b Fr(j)1142 4028 y Ft(2)1212 3942 y Fq(Z)1303 3968 y Fp(1)1263 4148 y(\0001)1407 4066 y Fs(e)1449 4028 y Fo(iS)t Ft(\()p Fo(x;u)p Ft(\))1695 4066 y Fs(e)1737 4028 y Fp(\000)p Fo(iS)t Ft(\()p Fo(x)1930 4005 y Fl(0)1952 4028 y Fo(;u)p Ft(\))2059 4066 y Fs(du)26 b Fv(=)f Fs(\016)s Fv(\()p Fs(x)c Fr(\000)f Fs(x)2574 4028 y Fp(0)2597 4066 y Fv(\))31 b Fs(:)810 b Fv(\(3.5\))24 4300 y(It)30 b(implies)e Fs(C)j Fv(=)25 b Fs(e)665 4267 y Fo(i\013)754 4300 y Fs(C)819 4314 y Ft(0)859 4300 y Fv(,)30 b(where)g Fs(\013)h Fv(is)e(an)i(arbitrary)e(phase)h(and)1545 4524 y Fs(C)1610 4538 y Ft(0)1674 4524 y Fv(=)1770 4423 y Fq(\020)1878 4463 y Fs(\015)p 1835 4503 140 4 v 1835 4586 a Fv(2)p Fs(\031)1935 4560 y Ft(2)1984 4423 y Fq(\021)2049 4419 y Fk(1)p 2049 4431 31 3 v 2049 4472 a(4)2139 4524 y Fs(;)1334 b Fv(\(3.6\))24 4723 y(In)24 b(the)i(next)g(section)f(it)g (w)m(ould)f(b)s(e)h(clear)g(that)h(a)g(natural)f(c)m(hoice)h(for)f(the) h(phase)f(is)f Fs(\013)i Fv(=)f Fr(\000)p Fs(\031)s(=)p Fv(8.)40 b(Clearly)-8 b(,)24 4836 y Fr(U)39 b Fv(ma)m(y)31 b(b)s(e)f(extended)g(to)h(act)h(on)e Fr(S)7 b Fv(\()p Fn(R)1373 4850 y Fo(u)1424 4836 y Fv(\))1459 4803 y Fp(0)1482 4836 y Fv(.)41 b(It)30 b(is)g(easy)h(to)g(sho)m(w)f(that)1432 5009 y Fr(U)9 b Fv(\()p Fr(S)e Fv(\()p Fn(R)1690 5023 y Fo(u)1741 5009 y Fv(\))1776 4971 y Fp(0)1799 5009 y Fv(\))26 b Fr(\032)f(S)7 b Fv(\()p Fn(R)2113 5023 y Fo(x)2163 5009 y Fv(\))2198 4971 y Fp(0)2252 5009 y Fs(:)1221 b Fv(\(3.7\))1832 5281 y(4)p eop %%Page: 5 5 5 4 bop 24 44 a Fw(Prop)s(osition)36 b(2)46 b Ff(The)32 b(gener)-5 b(alize)g(d)35 b(eigenve)-5 b(ctors)33 b Fg(f)1874 11 y Fp(\006)1874 67 y Fo(n)1957 44 y Fr(2)25 b(S)7 b Fv(\()p Fn(R)2200 58 y Fo(x)2250 44 y Fv(\))2285 11 y Fp(0)2341 44 y Ff(and)34 b Fs(f)2573 11 y Fp(\006)2563 67 y Fo(n)2656 44 y Fr(2)25 b(S)7 b Fv(\()p Fn(R)2899 58 y Fo(u)2950 44 y Fv(\))2985 11 y Fp(0)3041 44 y Ff(ar)-5 b(e)34 b(r)-5 b(elate)g(d)34 b(by:)1623 218 y Fg(f)1653 181 y Fp(\006)1653 241 y Fo(n)1737 218 y Fv(=)25 b Fr(U)f Fs(f)1969 181 y Fp(\006)1959 241 y Fo(n)2060 218 y Fs(:)1413 b Fv(\(3.8\))24 400 y Ff(Pr)-5 b(o)g(of)p Fv(.)42 b(Let)31 b(us)e(sho)m(w)i(that)g Fg(f)1033 367 y Ft(+)1033 423 y Fo(n)1117 400 y Fv(=)24 b Fr(U)9 b Fs(f)1333 367 y Ft(+)1323 423 y Fo(n)1392 400 y Fv(,)30 b(that)h(is)1357 616 y Fg(f)1387 578 y Ft(+)1387 638 y Fo(n)1445 616 y Fv(\()p Fs(x)p Fv(\))42 b Fr(\030)1720 492 y Fq(Z)1826 616 y Fs(u)1878 578 y Fo(n)1925 616 y Fs(e)1967 578 y Fo(iS)t Ft(\()p Fo(x;u)p Ft(\))2197 616 y Fs(du)31 b(:)1146 b Fv(\(3.9\))24 832 y(Using)29 b(the)i(de\014nition)d(of)i Fs(S)5 b Fv(\()p Fs(x;)15 b(u)p Fv(\))32 b(one)e(has)475 925 y Fq(Z)581 1049 y Fs(u)633 1011 y Fo(n)680 1049 y Fs(e)722 1011 y Fo(iS)t Ft(\()p Fo(x;u)p Ft(\))952 1049 y Fs(du)83 b Fv(=)1288 948 y Fq(\020)1342 1049 y Fr(\000)p Fs(i)1444 969 y Fq(p)p 1535 969 153 4 v 80 x Fv(2)p Fs(\031)s(\015)1688 948 y Fq(\021)1742 970 y Fp(\000)p Fo(n)1859 1049 y Fs(e)1901 1011 y Fo(i\015)1976 984 y Fh(x)2011 963 y Fk(2)p 1976 996 70 3 v 1995 1037 a(2)2111 987 y Fs(d)2158 954 y Fo(n)p 2085 1028 147 4 v 2085 1111 a Fs(dx)2184 1085 y Fo(n)2256 925 y Fq(Z)2362 1049 y Fs(e)2404 1011 y Fo(iu)2469 988 y Fk(2)2504 1011 y Fo(=)p Ft(2)p Fp(\000)p Fo(i)2653 963 y Fp(p)p 2712 963 76 3 v 48 x Ft(2)p Fo(\015)5 b(xu)2872 1049 y Fs(du)1134 1292 y Fv(=)1288 1215 y Fr(p)p 1364 1215 203 4 v 77 x(\000)p Fv(2)p Fs(\031)s(i)1582 1191 y Fq(\020)1636 1292 y Fr(\000)p Fs(i)1738 1212 y Fq(p)p 1829 1212 153 4 v 80 x Fv(2)p Fs(\031)s(\015)1982 1191 y Fq(\021)2036 1214 y Fp(\000)p Fo(n)2153 1292 y Fs(e)2195 1254 y Fp(\000)p Fo(i\015)2324 1227 y Fh(x)2359 1206 y Fk(2)p 2324 1239 70 3 v 2344 1280 a(2)2423 1164 y Fq(\022)2505 1292 y Fs(e)2547 1254 y Fo(i\015)t(x)2651 1231 y Fk(2)2726 1230 y Fs(d)2773 1197 y Fo(n)p 2700 1271 147 4 v 2700 1354 a Fs(dx)2799 1328 y Fo(n)2856 1292 y Fs(e)2898 1254 y Fp(\000)p Fo(i\015)t(x)3057 1231 y Fk(2)3096 1164 y Fq(\023)3209 1292 y Fs(:)219 b Fv(\(3.10\))24 1511 y(No)m(w,)31 b(due)f(to)h(the)f(w)m(ell)g(kno)m(wn)g(form)m(ula)f(for)h(the)h (Hermite)f(p)s(olynomials)1281 1722 y Fs(e)1323 1685 y Fo(iz)1383 1661 y Fk(2)42 b Fs(d)1502 1628 y Fo(n)p 1432 1702 141 4 v 1432 1785 a Fs(dz)1525 1759 y Fo(n)1582 1722 y Fs(e)1624 1685 y Fp(\000)p Fo(iz)1739 1661 y Fk(2)1803 1722 y Fv(=)25 b(\()p Fr(\000)p Fv(1\))2085 1685 y Fo(n)2133 1722 y Fs(H)2209 1736 y Fo(n)2255 1722 y Fv(\()p Fs(z)t Fv(\))32 b Fs(;)1025 b Fv(\(3.11\))24 1917 y(one)30 b(obtains)662 1956 y Fq(Z)768 2080 y Fs(u)820 2042 y Fo(n)867 2080 y Fs(e)909 2042 y Fo(iS)t Ft(\()p Fo(x;u)p Ft(\))1139 2080 y Fs(du)25 b Fv(=)1359 2003 y Fr(p)p 1435 2003 203 4 v 77 x(\000)p Fv(2)p Fs(\031)s(i)1653 1952 y Fq(\022)1737 2018 y Fs(i)p 1730 2059 46 4 v 1730 2142 a Fv(2)1785 1952 y Fq(\023)1852 1974 y Fp(\000)1917 1947 y Fh(n)p 1917 1959 39 3 v 1921 2000 a Fk(2)1985 2080 y Fs(e)2027 2042 y Fp(\000)p Fo(i\015)2156 2015 y Fh(x)2191 1994 y Fk(2)p 2156 2027 70 3 v 2175 2068 a(2)2239 2080 y Fs(H)2315 2094 y Fo(n)2362 2080 y Fv(\()2397 1999 y Fq(p)p 2488 1999 84 4 v 81 x Fs(i\015)6 b(x)p Fv(\))25 b Fr(\030)g Fg(f)2810 2042 y Ft(+)2810 2102 y Fo(n)2869 2080 y Fv(\()p Fs(x)p Fv(\))31 b Fs(:)406 b Fv(\(3.12\))24 2289 y(T)-8 b(o)30 b(pro)m(v)m(e)i(that)f Fg(f)630 2256 y Fp(\000)630 2311 y Fo(n)714 2289 y Fv(=)25 b Fr(U)9 b Fs(f)931 2256 y Fp(\000)921 2311 y Fo(n)989 2289 y Fv(,)30 b(let)h(us)e(note)i(that) 1660 2256 y Ft(2)1163 2534 y Fg(f)1193 2496 y Fp(\000)1193 2556 y Fo(n)1252 2534 y Fv(\()p Fs(x)p Fv(\))26 b(=)p 1496 2445 212 4 v 25 w Fg(f)1526 2496 y Ft(+)1526 2546 y Fo(n)1584 2534 y Fv(\()p Fs(x)p Fv(\))41 b Fr(\030)1859 2410 y Fq(Z)1965 2534 y Fs(u)2017 2496 y Fo(n)2064 2534 y Fs(e)2106 2496 y Fp(\000)p Fo(iS)t Ft(\()p Fo(x;u)p Ft(\))2391 2534 y Fs(du)30 b(:)908 b Fv(\(3.13\))24 2733 y(No)m(w,)31 b(taking)f(in)m(to)h(accoun)m(t)g(that)g Fs(f)1308 2700 y Ft(+)1298 2755 y Fo(n)1397 2733 y Fv(and)f Fs(f)1629 2700 y Fp(\000)1619 2755 y Fo(n)1717 2733 y Fv(are)h(related)g(b)m(y)f(the)g(F)-8 b(ourier)30 b(transformation)1216 2906 y Fs(u)1268 2869 y Fo(n)1340 2906 y Fv(=)1436 2827 y Fr(p)p 1512 2827 101 4 v 79 x Fv(2)p Fs(\031)s Fv(\()p Fr(\000)p Fs(i)p Fv(\))1784 2869 y Fo(n)1832 2906 y Fs(F)1903 2869 y Fp(\000)p Ft(1)1997 2906 y Fv([)p Fs(\016)2065 2869 y Ft(\()p Fo(n)p Ft(\))2168 2906 y Fv(\()p Fs(k)s Fv(\)]\()p Fs(u)p Fv(\))j Fs(;)960 b Fv(\(3.14\))24 3080 y(one)30 b(obtains)659 3150 y Fq(Z)765 3274 y Fs(u)817 3236 y Fo(n)864 3274 y Fs(e)906 3236 y Fp(\000)p Fo(iS)t Ft(\()p Fo(x;u)p Ft(\))1191 3274 y Fs(du)84 b Fv(=)1527 3194 y Fr(p)p 1603 3194 V 80 x Fv(2)p Fs(\031)t Fv(\()p Fr(\000)p Fs(i)p Fv(\))1876 3236 y Fo(n)1939 3150 y Fq(Z)2045 3274 y Fs(\016)2088 3236 y Ft(\()p Fo(n)p Ft(\))2190 3274 y Fv(\()p Fs(u)p Fv(\))p Fs(F)2383 3236 y Fp(\000)p Ft(1)2494 3200 y Fq(\002)2532 3274 y Fs(e)2574 3236 y Fp(\000)p Fo(iS)2704 3200 y Fq(\003)2757 3274 y Fv(\()p Fs(u)p Fv(\))15 b Fs(du)31 b(:)404 b Fv(\(3.15\))24 3484 y(Finally)-8 b(,)627 3695 y Fs(F)698 3658 y Fp(\000)p Ft(1)807 3622 y Fq(\002)845 3695 y Fs(e)887 3658 y Fp(\000)p Fo(iS)1017 3622 y Fq(\003)1070 3695 y Fv(\()p Fs(u)p Fv(\))26 b(=)1390 3634 y(1)p 1324 3674 177 4 v 1324 3692 a Fr(p)p 1400 3692 101 4 v 76 x Fv(2)p Fs(\031)1526 3571 y Fq(Z)1632 3695 y Fs(e)1674 3658 y Fp(\000)p Fo(ik)r(u)1852 3695 y Fs(e)1894 3658 y Fp(\000)p Fo(iS)t Ft(\()p Fo(x;k)r Ft(\))2176 3695 y Fs(dk)j Fv(=)2395 3619 y Fr(p)p 2471 3619 103 4 v 76 x(\000)p Fs(i)15 b(e)2630 3658 y Fo(iS)t Ft(\()p Fo(x;u)p Ft(\))2891 3695 y Fs(;)537 b Fv(\(3.16\))24 3912 y(and)29 b(hence)1272 4044 y Fg(f)1302 4007 y Fp(\000)1302 4067 y Fo(n)1361 4044 y Fv(\()p Fs(x)p Fv(\))41 b Fr(\030)1635 3920 y Fq(Z)1741 4044 y Fs(\016)1784 4007 y Ft(\()p Fo(n)p Ft(\))1887 4044 y Fv(\()p Fs(u)p Fv(\))p Fs(e)2051 4007 y Fo(iS)t Ft(\()p Fo(x;u)p Ft(\))2282 4044 y Fs(du)30 b(;)1017 b Fv(\(3.17\))24 4233 y(whic)m(h)29 b(ends)g(the)i(pro)s(of.) 2736 b Fe(2)p 24 4302 1465 4 v 127 4356 a Fk(2)162 4387 y Fj(It)25 b(turns)g(out)h(that)f(a)h(function)1098 4519 y Fd(e)1088 4538 y Fi(S)t Fj(\()p Fi(x;)12 b(v)s Fj(\))21 b(=)h Fc(\000)p Fi(S)t Fj(\()p Fi(x;)12 b(v)s Fj(\))21 b(=)g Fc(\000)1879 4490 y Fi(\015)p 1879 4521 44 4 v 1882 4589 a Fj(2)1933 4538 y Fi(x)1977 4502 y Fk(2)2028 4538 y Fj(+)2105 4473 y Fd(p)p 2182 4473 83 4 v 65 x Fj(2)p Fi(\015)t(xv)e Fc(\000)2451 4490 y Fj(1)p 2451 4521 39 4 v 2451 4589 a(2)2500 4538 y Fi(v)2540 4502 y Fk(2)2600 4538 y Fi(;)24 4700 y Fj(serv)n(es)26 b(as)g(a)g (generating)h(function)e(for)i(the)e(canonical)i(transformation)g (\(1.4\):)1393 4894 y Fi(p)21 b Fj(=)1544 4846 y Fi(@)1600 4827 y Fd(e)1589 4846 y Fi(S)p 1544 4877 97 4 v 1548 4945 a(@)t(x)1676 4894 y(;)249 b(u)22 b Fj(=)f Fc(\000)2163 4846 y Fi(@)2218 4827 y Fd(e)2208 4846 y Fi(S)p 2163 4877 V 2169 4945 a(@)t(v)2294 4894 y(:)1832 5281 y Fv(5)p eop %%Page: 6 6 6 5 bop 24 44 a Fu(4)134 b(Energy)46 b(eigenstates)24 247 y Fv(The)22 b(sp)s(ectrum)f(of)i(the)g(self-adjoin)m(t)f(op)s (erator)h(\(1.2\))i(reads)e Fs(\033)s Fv(\()2208 224 y Fq(b)2187 247 y Fs(H)7 b Fv(\))26 b(=)f(\()p Fr(\0001)p Fs(;)15 b Fr(1)p Fv(\))23 b(and)f(the)h(corresp)s(onding)24 360 y(energy)30 b(eigenstates)i(\(in)d Fs(u)p Fv(-represen)m(tation\))i (are)g(giv)m(en)g(b)m(y)f(\(cf.)41 b(section)31 b(6)f(in)f([1)q(]\):) 1271 602 y Fs( )1333 565 y Fo(E)1330 625 y Fp(\006)1393 602 y Fv(\()p Fs(u)p Fv(\))d(=)1738 541 y(1)p 1647 582 229 4 v 1647 600 a Fr(p)p 1723 600 153 4 v 66 x Fv(2)p Fs(\031)s(\015)1900 602 y(u)1952 555 y Fp(\000)p Ft(\()p Fo(iE)t(=\015)t Ft(+1)p Fo(=)p Ft(2\))1952 626 y Fp(\006)2412 602 y Fs(;)1061 b Fv(\(4.1\))24 866 y(with)35 b Fs(E)42 b Fr(2)36 b Fn(R)s Fv(.)67 b(F)-8 b(or)37 b(the)h(basic)e(prop)s (erties)g(of)h(the)g(temp)s(ered)f(distributions)e Fs(u)2869 833 y Fo(\025)2869 888 y Fp(\006)2964 866 y Fr(2)i(S)7 b Fv(\()p Fn(R)3218 880 y Fo(u)3269 866 y Fv(\))3304 833 y Fp(0)3365 866 y Fv(w)m(e)37 b(refer)24 979 y(the)44 b(reader)g(to)h([14)q(,)f(15)q(])h(\(see)g(also)f(the)g(App)s(endix)e (in)h([1]\).)83 b(No)m(w,)48 b(using)43 b(\()p Fs(x;)15 b(p)p Fv(\))45 b(co)s(ordinates)f(the)24 1092 y(corresp)s(onding)28 b(eigen)m(v)-5 b(alue)30 b(problem)1406 1056 y Ft(1)p 1406 1071 36 4 v 1406 1123 a(2)1451 1092 y Fv(\()5 b Fq(b)-56 b Fs(p)1532 1059 y Ft(2)1592 1092 y Fr(\000)20 b Fs(\015)1735 1059 y Ft(2)1778 1092 y Fq(b)-54 b Fs(x)1827 1059 y Ft(2)1866 1092 y Fv(\))p Fs(\037)1958 1059 y Fo(E)2043 1092 y Fv(=)25 b Fs(E)5 b(\037)2268 1059 y Fo(E)2358 1092 y Fv(reads)1161 1305 y Fs(@)1214 1268 y Ft(2)1209 1328 y Fo(x)1254 1305 y Fs(\037)1311 1268 y Fo(E)1370 1305 y Fv(\()p Fs(x)p Fv(\))21 b(+)f(\()p Fs(\015)1691 1268 y Ft(2)1731 1305 y Fs(x)1783 1268 y Ft(2)1842 1305 y Fv(+)g(2)p Fs(E)5 b Fv(\))p Fs(\037)2142 1268 y Fo(E)2203 1305 y Fv(\()p Fs(x)p Fv(\))26 b(=)f(0)31 b Fs(:)950 b Fv(\(4.2\))24 1510 y(In)m(tro)s(ducing)28 b(a)j(new)f(v)-5 b(ariable)1599 1623 y Fs(z)30 b Fv(=)1767 1542 y Fq(p)p 1858 1542 129 4 v 81 x Fv(2)p Fs(i\015)21 b(x)30 b(;)1389 b Fv(\(4.3\))24 1789 y(the)30 b(ab)s(o)m(v)m(e)i(equation)e(ma)m(y)h(b) s(e)f(rewritten)f(as)i(follo)m(ws)1228 2044 y Fs(@)1281 2007 y Ft(2)1276 2067 y Fo(z)1321 2044 y Fs(\037)1378 2007 y Fo(E)1458 2044 y Fv(+)1549 1916 y Fq(\022)1616 2044 y Fs(\027)26 b Fv(+)1787 1983 y(1)p 1787 2023 46 4 v 1787 2106 a(2)1863 2044 y Fr(\000)1964 1983 y Fs(z)2010 1950 y Ft(2)p 1964 2023 86 4 v 1984 2106 a Fv(4)2060 1916 y Fq(\023)2142 2044 y Fs(\037)2199 2007 y Fo(E)2283 2044 y Fv(=)f(0)31 b Fs(;)1018 b Fv(\(4.4\))24 2293 y(with)1473 2433 y Fs(\027)31 b Fv(=)25 b Fr(\000)1731 2305 y Fq(\022)1798 2433 y Fs(i)1839 2372 y(E)p 1839 2412 73 4 v 1849 2496 a(\015)1942 2433 y Fv(+)2042 2372 y(1)p 2042 2412 46 4 v 2042 2496 a(2)2098 2305 y Fq(\023)2210 2433 y Fs(;)1263 b Fv(\(4.5\))24 2650 y(whic)m(h)32 b(is)i(the)g(de\014ning)e(equation)i (for)g(the)g(parab)s(olic)f(cylinder)f(functions)h([18)q(,)h(19)q(,)g (20)q(].)52 b(Its)34 b(solution)24 2763 y Fs(\037)81 2730 y Fo(E)140 2763 y Fv(\()p Fs(z)t Fv(\))c(is)e(a)h(linear)e(com)m (bination)h(of)h Fs(D)1394 2777 y Fo(\027)1438 2763 y Fv(\()p Fs(z)t Fv(\),)h Fs(D)1684 2777 y Fo(\027)1728 2763 y Fv(\()p Fr(\000)p Fs(z)t Fv(\),)g Fs(D)2045 2777 y Fp(\000)p Fo(\027)t Fp(\000)p Ft(1)2233 2763 y Fv(\()p Fs(iz)t Fv(\))g(and)f Fs(D)2661 2777 y Fp(\000)p Fo(\027)t Fp(\000)p Ft(1)2849 2763 y Fv(\()p Fr(\000)p Fs(iz)t Fv(\).)3092 2730 y Ft(3)3173 2763 y Fv(On)f(the)h(other)24 2876 y(hand)42 b(the)h(energy)h(eigenstates)h(in)d Fs(x)p Fv(-represen)m(tation)h Fs(\037)2076 2843 y Fo(E)2136 2876 y Fv(\()p Fs(x)p Fv(\))h(ma)m(y)g(b)s(e)f(obtained)f(b)m(y)i (applying)d(the)24 2989 y(op)s(erator)30 b Fr(U)40 b Fv(de\014ned)29 b(in)g(\(3.4\))j(to)f(the)g(corresp)s(onding)d (eigenstates)k(in)d Fs(u)p Fv(-represen)m(tation)h Fs( )3280 2956 y Fo(E)3277 3011 y Fp(\006)3340 2989 y Fv(\()p Fs(u)p Fv(\):)931 3244 y Fs(\037)988 3206 y Fo(E)988 3266 y Fp(\006)1047 3244 y Fv(\()p Fs(x)p Fv(\))c(=)f(\()p Fr(U)9 b Fs( )1454 3206 y Fo(E)1451 3266 y Fp(\006)1514 3244 y Fv(\)\()p Fs(x)p Fv(\))27 b(=)e Fs(C)1880 3120 y Fq(Z)1971 3146 y Fp(1)1931 3326 y(\0001)2076 3244 y Fs( )2138 3206 y Fo(E)2135 3266 y Fp(\006)2198 3244 y Fv(\()p Fs(u)p Fv(\))15 b Fs(e)2377 3206 y Fo(iS)t Ft(\()p Fo(x;u)p Ft(\))2623 3244 y Fs(du)31 b(:)720 b Fv(\(4.6\))24 3495 y(Hence)877 3721 y Fs(\037)934 3683 y Fo(E)934 3743 y Ft(+)993 3721 y Fv(\()p Fs(x)p Fv(\))84 b(=)1441 3659 y Fs(C)p 1362 3700 229 4 v 1362 3718 a Fr(p)p 1438 3718 153 4 v 66 x Fv(2)p Fs(\031)s(\015)1616 3721 y(e)1658 3683 y Fo(i)1692 3652 y Fh(\015)p 1692 3668 36 3 v 1695 3709 a Fk(2)1738 3683 y Fo(x)1778 3660 y Fk(2)1832 3597 y Fq(Z)1923 3623 y Fp(1)1882 3803 y Ft(0)2012 3721 y Fs(u)2064 3683 y Fo(\027)2123 3721 y Fs(e)2165 3683 y Fp(\000)p Fo(i)2244 3635 y Fp(p)p 2303 3635 76 3 v 48 x Ft(2)p Fo(\015)t(xu)p Ft(+)p Fo(iu)2579 3660 y Fk(2)2613 3683 y Fo(=)p Ft(2)2703 3721 y Fs(du)1199 3964 y Fv(=)1441 3903 y Fs(C)p 1362 3944 229 4 v 1362 3962 a Fr(p)p 1438 3962 153 4 v 66 x Fv(2)p Fs(\031)s(\015)1616 3884 y Fr(p)p 1692 3884 32 4 v 80 x Fs(i)1723 3903 y Fo(\027)t Ft(+1)1872 3964 y Fs(e)1914 3927 y Fp(\000)1979 3896 y Fh(y)2013 3875 y Fk(2)p 1979 3912 68 3 v 1998 3953 a(4)2076 3841 y Fq(Z)2167 3867 y Fp(1)2126 4047 y Ft(0)2257 3964 y Fs(\030)2301 3927 y Fo(\027)2359 3964 y Fs(e)2401 3927 y Fo(y)r(\030)s Fp(\000)p Fo(\030)2561 3904 y Fk(2)2595 3927 y Fo(=)p Ft(2)2685 3964 y Fs(d\030)35 b(;)666 b Fv(\(4.7\))24 4224 y(with)24 b Fs(y)k Fv(=)395 4157 y Fr(p)p 471 4157 200 4 v 67 x(\000)p Fv(2)p Fs(i\015)21 b(x)p Fv(,)27 b(and)e(using)g(an)g(in)m(tegral)h(represen)m(tation)g (for)g Fs(D)2444 4238 y Fo(p)2484 4224 y Fv(\()p Fs(y)s Fv(\))g(\(form)m(ula)g(9.241\(2\))j(in)c([18)q(]\):)3645 4191 y Ft(4)1054 4532 y Fs(D)1129 4546 y Fo(p)1169 4532 y Fv(\()p Fs(y)s Fv(\))g(=)1446 4470 y Fs(e)1488 4434 y Fp(\000)1553 4404 y Fh(y)1587 4383 y Fk(2)p 1553 4419 68 3 v 1572 4460 a(4)p 1418 4511 244 4 v 1418 4594 a Fv(\000\()p Fr(\000)p Fs(p)p Fv(\))1703 4408 y Fq(Z)1793 4434 y Fp(1)1753 4614 y Ft(0)1883 4532 y Fs(\030)1927 4494 y Fp(\000)p Fo(p)p Fp(\000)p Ft(1)2127 4532 y Fs(e)2169 4494 y Fp(\000)p Fo(y)r(\030)s Fp(\000)p Fo(\030)2384 4471 y Fk(2)2418 4494 y Fo(=)p Ft(2)2508 4532 y Fs(d\030)35 b(;)843 b Fv(\(4.8\))p 24 4678 1465 4 v 127 4732 a Fk(3)162 4764 y Fj(These)26 b(four)g(functions)g(are)h(linearly)f(dep)r(enden)n (t.)33 b(F)-6 b(or)26 b(the)f(linear)i(relation)f(see)h(e.g.)35 b(form)n(ula)26 b(9.248)h(in)f([18)q(].)127 4823 y Fk(4)162 4855 y Fj(The)g(v)l(alidit)n(y)f(of)i(this)f(form)n(ula)g(is)g (restricted)g(in)g([18)q(])g(for)h(Re)13 b Fi(p)21 b(<)g Fj(0.)36 b(Ho)n(w)n(ev)n(er,)26 b(as)g(w)n(e)g(shall)h(sho)n(w)g(\(see) f(the)f(pro)r(of)i(of)24 4946 y(Prop)r(osition)g(4\),)f(it)g(is)g(v)l (alid)g(for)g(all)h Fi(p)21 b Fc(2)g Fb(C)12 b Fj(.)1832 5281 y Fv(6)p eop %%Page: 7 7 7 6 bop 24 44 a Fv(one)30 b(\014nds)838 176 y Fs(\037)895 139 y Fo(E)895 199 y Ft(+)955 176 y Fv(\()p Fs(x)p Fv(\))c(=)1271 115 y Fs(C)1336 129 y Ft(0)p 1209 155 229 4 v 1209 173 a Fr(p)p 1284 173 153 4 v 1284 240 a Fv(2)p Fs(\031)s(\015)1462 96 y Fr(p)p 1538 96 32 4 v 80 x Fs(i)1569 115 y Fo(\027)t Ft(+)1673 88 y Fk(1)p 1673 100 31 3 v 1673 141 a(2)1733 176 y Fv(\000\()p Fs(\027)g Fv(+)20 b(1\))p Fs(D)2142 190 y Fp(\000)p Fo(\027)t Fp(\000)p Ft(1)2331 176 y Fv(\()p Fr(\000)2437 96 y Fq(p)p 2528 96 200 4 v 80 x Fr(\000)p Fv(2)p Fs(i\015)6 b(x)p Fv(\))30 b Fs(;)628 b Fv(\(4.9\))24 393 y(with)29 b Fs(\027)36 b Fv(giv)m(en)30 b(in)f(\(4.5\).)43 b(Similarly)-8 b(,)27 b(using)i(an)h(ob)m(vious)g(relation)f(\()p Fr(\000)p Fs(u)p Fv(\))2531 360 y Fo(\025)2531 416 y Ft(+)2616 393 y Fv(=)c Fs(u)2764 360 y Fo(\025)2764 416 y Fp(\000)2823 393 y Fv(,)31 b(one)f(obtains:)858 628 y Fs(\037)915 590 y Fo(E)915 650 y Fp(\000)975 628 y Fv(\()p Fs(x)p Fv(\))c(=)1291 566 y Fs(C)1356 580 y Ft(0)p 1229 607 229 4 v 1229 625 a Fr(p)p 1304 625 153 4 v 1304 691 a Fv(2)p Fs(\031)s(\015)1482 547 y Fr(p)p 1558 547 32 4 v 81 x Fs(i)1620 567 y Fo(\027)t Ft(+)1724 539 y Fk(1)p 1724 551 31 3 v 1724 593 a(2)1783 628 y Fv(\000\()p Fs(\027)g Fv(+)20 b(1\))p Fs(D)2192 642 y Fp(\000)p Fo(\027)t Fp(\000)p Ft(1)2382 628 y Fv(\()2417 547 y Fq(p)p 2508 547 200 4 v 81 x Fr(\000)p Fv(2)p Fs(i\015)5 b(x)p Fv(\))31 b Fs(;)603 b Fv(\(4.10\))24 872 y(that)34 b(is,)f Fs(\037)401 839 y Fo(E)401 895 y Fp(\000)460 872 y Fv(\()p Fs(x)p Fv(\))e(=)f Fs(\037)771 839 y Fo(E)771 895 y Ft(+)831 872 y Fv(\()p Fr(\000)p Fs(x)p Fv(\).)50 b(Actually)-8 b(,)34 b(instead)f(of)g Fs(\037)1969 839 y Fo(E)1969 895 y Fp(\006)2062 872 y Fv(one)g(ma)m(y)h(use)f(energy)h(eigenstates)h (with)d(the)24 985 y(de\014nite)d(parit)m(y:)1302 1205 y Fs(\037)1359 1167 y Fo(E)1359 1227 y Ft(ev)n(en)1583 1205 y Fv(=)1785 1143 y(1)p 1747 1184 122 4 v 1747 1202 a Fr(p)p 1823 1202 46 4 v 75 x Fv(2)1893 1131 y Fq(\000)1935 1205 y Fs(\037)1992 1167 y Fo(E)1992 1227 y Ft(+)2072 1205 y Fv(+)20 b Fs(\037)2220 1167 y Fo(E)2220 1227 y Fp(\000)2279 1131 y Fq(\001)2366 1205 y Fs(;)1062 b Fv(\(4.11\))1324 1443 y Fs(\037)1381 1405 y Fo(E)1381 1466 y Ft(o)r(dd)1583 1443 y Fv(=)1785 1381 y(1)p 1747 1422 122 4 v 1747 1440 a Fr(p)p 1823 1440 46 4 v 75 x Fv(2)1893 1369 y Fq(\000)1935 1443 y Fs(\037)1992 1405 y Fo(E)1992 1465 y Ft(+)2072 1443 y Fr(\000)20 b Fs(\037)2220 1405 y Fo(E)2220 1465 y Fp(\000)2279 1369 y Fq(\001)2366 1443 y Fs(;)1062 b Fv(\(4.12\))24 1672 y(that)31 b(is,)1055 1785 y Fw(P)15 b Fs(\037)1198 1747 y Fo(E)1198 1807 y Ft(ev)n(en)1365 1785 y Fv(=)25 b Fs(\037)1518 1747 y Fo(E)1518 1807 y Ft(ev)n(en)1690 1785 y Fs(;)251 b Fw(P)15 b Fs(\037)2109 1747 y Fo(E)2109 1808 y Ft(o)r(dd)2255 1785 y Fv(=)25 b Fr(\000)p Fs(\037)2479 1747 y Fo(E)2479 1808 y Ft(o)r(dd)2628 1785 y Fs(;)800 b Fv(\(4.13\))24 1943 y(where)30 b Fw(P)g Fv(stands)g(for)g(the)h(parit)m(y)f(op)s(erator.)24 2138 y Fw(Prop)s(osition)36 b(3)46 b Ff(Ener)-5 b(gy)32 b(eigenstates)h Fs(\037)1510 2105 y Fo(E)1510 2160 y Fp(\006)1602 2138 y Ff(satisfy:)1163 2251 y Fq(Z)1254 2277 y Fp(1)1213 2457 y(\0001)p 1358 2287 240 4 v 1358 2375 a Fs(\037)1415 2343 y Fo(E)1415 2398 y Fp(\006)1475 2375 y Fv(\()p Fs(x)p Fv(\))p Fs(\037)1654 2337 y Fo(E)1710 2314 y Fl(0)1654 2397 y Fp(\006)1736 2375 y Fv(\()p Fs(x)p Fv(\))15 b Fs(dx)26 b Fv(=)f Fs(\016)s Fv(\()p Fs(E)i Fr(\000)20 b Fs(E)2429 2337 y Fp(0)2453 2375 y Fv(\))33 b Fs(;)907 b Fv(\(4.14\))24 2609 y Ff(and)1173 2620 y Fq(Z)1263 2646 y Fp(1)1223 2826 y(\0001)p 1368 2656 V 1368 2743 a Fs(\037)1425 2712 y Fo(E)1425 2767 y Fp(\006)1484 2743 y Fv(\()p Fs(x)p Fv(\))q Fs(\037)1664 2706 y Fo(E)1664 2766 y Fp(\006)1723 2743 y Fv(\()p Fs(x)1810 2706 y Fp(0)1834 2743 y Fv(\))15 b Fs(dE)31 b Fv(=)25 b Fs(\016)s Fv(\()p Fs(x)d Fr(\000)e Fs(x)2420 2706 y Fp(0)2443 2743 y Fv(\))33 b Fs(:)917 b Fv(\(4.15\))24 2986 y(The)30 b(pro)s(of)g(follo)m(ws)g (immediately)f(from)h(the)i(analogous)f(prop)s(erties)e(satis\014ed)h (b)m(y)h(energy)g(eigenstates)24 3099 y Fs( )86 3066 y Fo(E)83 3121 y Fp(\006)176 3099 y Fv(in)e Fs(u)p Fv(-represen)m (tation)i([1)q(].)165 3220 y(In)g([1)q(])h(w)m(e)h(ha)m(v)m(e)g(used)e (also)h(another)h(generalized)e(basis)g Fs(F)13 b Fv([)p Fs( )2338 3182 y Fp(\000)p Fo(E)2335 3243 y Fp(\006)2454 3220 y Fv(]\()p Fs(u)p Fv(\).)47 b(No)m(w,)33 b(w)m(e)g(\014nd)d(its)i Fr(U)41 b Fv(image)24 3333 y(in)29 b Fr(S)7 b Fv(\()p Fn(R)287 3347 y Fo(x)336 3333 y Fv(\))371 3300 y Fp(0)395 3333 y Fv(.)41 b(Recalling)29 b(the)i(F)-8 b(ourier)29 b(transformation)h(of)h Fs(x)2103 3300 y Fo(\025)2103 3355 y Fp(\006)2192 3333 y Fv(\(see)g([14)q(])g(and)f(App)s(endix)d(in) i([1)q(]\):)944 3566 y Fs(F)13 b Fv([)p Fs(x)1092 3528 y Fo(\025)1092 3588 y Fp(\006)1151 3566 y Fv(]\()p Fs(u)p Fv(\))26 b(=)1467 3504 y Fr(\006)p Fs(i)p 1430 3545 177 4 v 1430 3563 a Fr(p)p 1506 3563 101 4 v 75 x Fv(2)p Fs(\031)1632 3566 y(e)1674 3528 y Fp(\006)p Fo(i\025)1804 3501 y Fh(\031)p 1804 3513 38 3 v 1808 3554 a Fk(2)1871 3566 y Fv(\000\()p Fs(\025)21 b Fv(+)f(1\)\()p Fs(u)h Fv(+)f Fs(i)p Fv(0\))2518 3528 y Fp(\000)p Fo(\025)p Fp(\000)p Ft(1)2740 3566 y Fs(:)688 b Fv(\(4.16\))24 3795 y(one)30 b(has)997 3933 y Fs(F)13 b Fv([)p Fs( )1155 3895 y Fp(\000)p Fo(E)1152 3956 y Ft(+)1270 3933 y Fv(]\()p Fs(u)p Fv(\))26 b(=)1641 3871 y(1)p 1549 3912 229 4 v 1549 3930 a Fr(p)p 1625 3930 153 4 v 67 x Fv(2)p Fs(\031)s(\015)1813 3871 y Fv(\()p Fr(\000)p Fs(i)p Fv(\))1985 3838 y Fo(\027)p 1813 3912 216 4 v 1832 3930 a Fr(p)p 1908 3930 101 4 v 75 x Fv(2)p Fs(\031)2054 3933 y Fv(\000\()p Fr(\000)p Fs(\027)6 b Fv(\)\()p Fs(u)20 b Fv(+)g Fs(i)p Fv(0\))2612 3895 y Fo(\027)2687 3933 y Fs(:)741 b Fv(\(4.17\))24 4134 y(Therefore,)30 b(the)h(corresp)s(onding)d Fs(x)p Fv(-represen)m(tation)1364 4320 y Fs(\021)1412 4283 y Fo(E)1409 4343 y Ft(+)1472 4320 y Fv(\()p Fs(x)p Fv(\))e(=)f(\()p Fr(U)f Fs(F)13 b Fv([)p Fs( )1990 4282 y Fp(\000)p Fo(E)1987 4344 y Ft(+)2106 4320 y Fv(]\)\()p Fs(x)p Fv(\))31 b Fs(;)1109 b Fv(\(4.18\))24 4507 y(is)29 b(giv)m(en)h(b)m(y)424 4736 y Fs(\021)472 4698 y Fo(E)469 4758 y Ft(+)532 4736 y Fv(\()p Fs(x)p Fv(\))84 b(=)980 4674 y Fs(C)p 902 4715 229 4 v 902 4733 a Fr(p)p 977 4733 153 4 v 977 4799 a Fv(2)p Fs(\031)s(\015)1165 4674 y Fv(\()p Fr(\000)p Fs(i)p Fv(\))1337 4641 y Fo(\027)p 1165 4715 216 4 v 1185 4733 a Fr(p)p 1261 4733 101 4 v 75 x Fv(2)p Fs(\031)1406 4736 y Fv(\000\()p Fr(\000)p Fs(\027)6 b Fv(\))1685 4612 y Fq(Z)1776 4638 y Fp(1)1736 4818 y(\0001)1866 4736 y Fv(\()p Fs(u)20 b Fv(+)g Fs(i)p Fv(0\))2175 4698 y Fo(\027)2219 4736 y Fs(e)2261 4698 y Fo(iS)t Ft(\()p Fo(x;u)p Ft(\))2492 4736 y Fs(du)738 4988 y Fv(=)980 4926 y Fs(C)p 902 4967 229 4 v 902 4985 a Fr(p)p 977 4985 153 4 v 977 5052 a Fv(2)p Fs(\031)s(\015)1165 4926 y Fv(\()p Fr(\000)p Fs(i)p Fv(\))1337 4893 y Fo(\027)p 1165 4967 216 4 v 1185 4985 a Fr(p)p 1261 4985 101 4 v 75 x Fv(2)p Fs(\031)1406 4988 y Fv(\(2)1486 4908 y Fr(p)p 1563 4908 32 4 v 1563 4988 a Fs(i)p Fv(\))1629 4950 y Fo(\027)t Ft(+1)1778 4988 y Fv(\000\()p Fr(\000)p Fs(\027)6 b Fv(\))15 b Fs(e)2094 4920 y Fh(y)2128 4899 y Fk(2)p 2094 4935 68 3 v 2113 4976 a(4)2191 4864 y Fq(Z)2282 4890 y Fp(1)2242 5070 y(\0001)2372 4988 y Fv(\()p Fs(\030)24 b Fv(+)c Fs(i)p Fv(0\))2673 4950 y Fo(\027)2732 4988 y Fs(e)2774 4950 y Fp(\000)p Ft(2)p Fo(\030)2898 4927 y Fk(2)2933 4950 y Fp(\000)p Ft(2)p Fo(iy)r(\030)3138 4988 y Fs(d\030)34 b(;)169 b Fv(\(4.19\))1832 5281 y(7)p eop %%Page: 8 8 8 7 bop 24 44 a Fv(with)29 b Fs(y)f Fv(=)400 -23 y Fr(p)p 475 -23 129 4 v 475 44 a Fv(2)p Fs(i\015)6 b(x)p Fv(.)41 b(No)m(w,)31 b(using)e(the)i(follo)m(wing)e(in)m(tegral)h(represen)m (tation)g(\(form)m(ula)g(9.241\(1\))k(in)29 b([18)q(]\))759 288 y Fs(D)834 302 y Fo(\027)877 288 y Fv(\()p Fs(y)s Fv(\))d(=)1169 226 y(1)p 1127 267 131 4 v 1127 285 a Fr(p)p 1203 285 56 4 v 66 x Fs(\031)1283 288 y Fv(2)1328 250 y Fo(\027)t Ft(+)1432 223 y Fk(1)p 1432 235 31 3 v 1432 276 a(2)1477 288 y Fv(\()p Fr(\000)p Fs(i)p Fv(\))1649 250 y Fo(\027)1693 288 y Fs(e)1745 220 y Fh(y)1779 199 y Fk(2)p 1745 235 68 3 v 1764 276 a(4)1857 164 y Fq(Z)1948 190 y Fp(1)1908 370 y(\0001)2037 288 y Fv(\()p Fs(\030)f Fv(+)20 b Fs(i)p Fv(0\))2339 250 y Fo(\027)2398 288 y Fs(e)2440 250 y Fp(\000)p Ft(2)p Fo(\030)2564 227 y Fk(2)2599 250 y Ft(+2)p Fo(iy)r(\030)2803 288 y Fs(d\030)35 b(;)503 b Fv(\(4.20\))24 535 y(one)30 b(obtains)978 667 y Fs(\021)1026 630 y Fo(E)1023 690 y Ft(+)1086 667 y Fv(\()p Fs(x)p Fv(\))c(=)1402 606 y Fs(C)1467 620 y Ft(0)p 1340 646 229 4 v 1340 665 a Fr(p)p 1416 665 153 4 v 66 x Fv(2)p Fs(\031)s(\015)1593 587 y Fr(p)p 1669 587 32 4 v 80 x Fs(i)1731 606 y Fo(\027)t Ft(+)1835 579 y Fk(1)p 1835 591 31 3 v 1835 632 a(2)1894 667 y Fv(\000\()p Fr(\000)p Fs(\027)6 b Fv(\))p Fs(D)2218 681 y Fo(\027)2262 667 y Fv(\()p Fr(\000)2368 587 y Fq(p)p 2459 587 129 4 v 80 x Fv(2)p Fs(i\015)g(x)p Fv(\))30 b Fs(:)723 b Fv(\(4.21\))24 875 y(Similarly)26 b(one)31 b(sho)m(ws)f(that)1364 988 y Fs(\021)1412 950 y Fo(E)1409 1010 y Fp(\000)1472 988 y Fv(\()p Fs(x)p Fv(\))c(=)f(\()p Fr(U)f Fs(F)13 b Fv([)p Fs( )1990 950 y Fp(\000)p Fo(E)1987 1011 y Fp(\000)2106 988 y Fv(]\)\()p Fs(x)p Fv(\))31 b Fs(;)1109 b Fv(\(4.22\))24 1152 y(is)29 b(giv)m(en)h(b)m(y)1013 1302 y Fs(\021)1061 1264 y Fo(E)1058 1324 y Fp(\000)1121 1302 y Fv(\()p Fs(x)p Fv(\))c(=)1437 1240 y Fs(C)1502 1254 y Ft(0)p 1375 1281 229 4 v 1375 1299 a Fr(p)p 1451 1299 153 4 v 67 x Fv(2)p Fs(\031)s(\015)1629 1222 y Fr(p)p 1705 1222 32 4 v 80 x Fs(i)1766 1241 y Fo(\027)t Ft(+)1870 1214 y Fk(1)p 1870 1226 31 3 v 1870 1267 a(2)1930 1302 y Fv(\000\()p Fr(\000)p Fs(\027)6 b Fv(\))p Fs(D)2254 1316 y Fo(\027)2297 1302 y Fv(\()2332 1221 y Fq(p)p 2423 1221 129 4 v 81 x Fv(2)p Fs(i\015)g(x)p Fv(\))31 b Fs(:)758 b Fv(\(4.23\))24 1510 y(Let)31 b(us)e(note,)i(that)p 1602 1553 208 4 v 1602 1623 a Fs(\027)26 b Fv(+)19 b(1)26 b(=)f Fr(\000)p Fs(\027)36 b(;)1346 b Fv(\(4.24\))24 1787 y(and)p 1480 1803 286 4 v 1480 1854 a Fr(p)p 1556 1854 32 4 v 80 x Fs(i)1618 1873 y Fo(\027)t Ft(+)1722 1846 y Fk(1)p 1721 1858 31 3 v 1721 1899 a(2)1791 1934 y Fv(=)1887 1854 y Fr(p)p 1963 1854 32 4 v 80 x Fs(i)2025 1873 y Fo(\027)t Ft(+)2129 1846 y Fk(1)p 2128 1858 31 3 v 2128 1899 a(2)2203 1934 y Fs(:)1225 b Fv(\(4.25\))24 2099 y(Clearly)-8 b(,)26 b(the)h(transition)f Fs(\027)18 b Fv(+)13 b(1)26 b Fr(\000)-16 b(!)26 b(\000)p Fs(\027)32 b Fv(is)26 b(equiv)-5 b(alen)m(t)26 b(to)h Fs(E)k Fr(\000)-15 b(!)25 b(\000)p Fs(E)32 b Fv(and)26 b(it)g(corresp)s(onds)g(to)h(the)g(fact)24 2212 y(that)245 2189 y Fq(b)223 2212 y Fs(H)7 b(\021)354 2179 y Fo(E)351 2234 y Ft(+)444 2212 y Fv(=)30 b Fr(\000)p Fs(E)5 b(\021)736 2179 y Fo(E)733 2234 y Ft(+)829 2212 y Fv(while)1090 2189 y Fq(b)1069 2212 y Fs(H)i(\037)1209 2179 y Fo(E)1209 2234 y Ft(+)1298 2212 y Fv(=)30 b(+)p Fs(E)5 b(\037)1599 2179 y Fo(E)1599 2234 y Ft(+)1658 2212 y Fv(.)49 b(The)33 b(symmetry)g(b)s(et)m(w)m(een)h Fs(\037)2761 2179 y Fo(E)2761 2234 y Fp(\006)2853 2212 y Fv(and)f Fs(\021)3081 2179 y Fo(E)3078 2234 y Fp(\006)3174 2212 y Fv(fully)e(justi\014es)24 2324 y(the)f(sp)s(eci\014c)f(c)m(hoice)j(of)e(the)h(phase)f(factor)h (in)e(the)i(constan)m(t)g Fs(C)7 b Fv(.)40 b(One)30 b(has)1531 2524 y Fs(\021)1579 2487 y Fo(E)1576 2547 y Fp(\006)1639 2524 y Fv(\()p Fs(x)p Fv(\))c(=)p 1883 2436 240 4 v 25 w Fs(\037)1940 2493 y Fo(E)1940 2547 y Fp(\006)1999 2524 y Fv(\()p Fs(x)p Fv(\))31 b Fs(;)1276 b Fv(\(4.26\))24 2724 y(that)25 b(is)g(they)g(are)h(related)f(b)m(y)g(the)g(time)g(rev)m (ersal)g(op)s(erator)h Fw(T)p Fv(:)38 b Fs(\021)2295 2691 y Fo(E)2292 2746 y Fp(\006)2380 2724 y Fv(=)25 b Fw(T)15 b Fs(\037)2621 2691 y Fo(E)2621 2746 y Fp(\006)2680 2724 y Fv(.)39 b(Th)m(us)24 b(energy)i(eigenstates)24 2837 y Fs(\021)72 2804 y Fo(E)69 2859 y Fp(\006)161 2837 y Fv(corresp)s(ond)i(to)j(the)e(time)h(rev)m(ersed)f(system.)41 b(This)28 b(w)m(a)m(y)i(all)f(four)f(solutions)g(of)i(\(4.4\))h(w)m (ere)f(used)f(to)24 2949 y(construct)h(four)g(families)e(of)j(energy)g (eigenstates:)41 b Fs(\037)1891 2916 y Fo(E)1891 2972 y Ft(+)1951 2949 y Fv(,)31 b Fs(\037)2064 2916 y Fo(E)2064 2972 y Fp(\000)2123 2949 y Fv(,)g Fs(\021)2227 2916 y Fo(E)2224 2972 y Ft(+)2317 2949 y Fv(and)f Fs(\021)2542 2916 y Fo(E)2539 2972 y Fp(\000)2602 2949 y Fv(.)24 3235 y Fu(5)134 b(Analytic)46 b(con)l(tin)l(uation,)g(resolv)l(en)l(t)h(and) e(resonances)24 3438 y Fv(No)m(w,)c(let)d(us)g(con)m(tin)m(ue)h(the)f (energy)h(eigenfunctions)e Fs(\037)2024 3405 y Fo(E)2024 3461 y Fp(\006)2122 3438 y Fv(and)h Fs(\021)2355 3405 y Fo(E)2352 3461 y Fp(\006)2453 3438 y Fv(in)m(to)g(the)h(energy)g (complex)f(plane)24 3551 y Fs(E)30 b Fr(2)25 b Fn(C)54 b Fv(and)30 b(let)g(us)g(study)f(its)h(analyticit)m(y)g(as)h(functions) e(of)h Fs(E)5 b Fv(.)24 3759 y Fw(Prop)s(osition)36 b(4)46 b Ff(The)32 b(p)-5 b(ar)g(ab)g(olic)36 b(cylinder)d(function)g Fs(D)2030 3774 y Fo(\025)2076 3759 y Fv(\()p Fs(z)t Fv(\))g Ff(is)g(an)g(analytic)h(function)e(of)h Fs(\025)26 b Fr(2)e Fn(C)18 b Ff(.)24 3967 y Fv(F)-8 b(or)40 b(the)g(pro)s(of)f(see) i(the)f(App)s(endix.)66 b(Due)40 b(to)h(the)f(ab)s(o)m(v)m(e)h(prop)s (osition)c(the)j(analytic)g(prop)s(erties)e(of)24 4080 y(the)32 b(energy)h(eigenfunctions)e(are)i(en)m(tirely)f(go)m(v)m (erned)i(b)m(y)e(the)h(analytic)f(prop)s(erties)f(of)i(the)g(\000)f (function)24 4193 y(whic)m(h)37 b(is)g(presen)m(t)h(in)f(the)h (de\014nition)e(of)i Fs(\037)1573 4160 y Fo(E)1573 4215 y Fp(\006)1671 4193 y Fv(and)f Fs(\021)1903 4160 y Fo(E)1900 4215 y Fp(\006)1963 4193 y Fv(.)64 b(Since)38 b(\000\()p Fs(\025)p Fv(\))g(has)g(simple)e(p)s(oles)h(at)i Fs(\025)g Fv(=)f Fr(\000)p Fs(n)p Fv(,)24 4305 y(with)31 b Fs(n)f Fv(=)f(0)p Fs(;)15 b Fv(1)p Fs(;)g Fv(2)p Fs(;)g(:)g(:)g(:)t Fv(,)34 b(functions)d Fs(\037)1292 4272 y Fo(E)1292 4328 y Fp(\006)1385 4305 y Fv(ha)m(v)m(e)j(p)s(oles)e(at)i Fs(E)h Fv(=)30 b Fr(\000)p Fs(E)2285 4319 y Fo(n)2331 4305 y Fv(,)k(whereas)f(functions)f Fs(\021)3180 4272 y Fo(E)3177 4328 y Fp(\006)3273 4305 y Fv(ha)m(v)m(e)i(p)s(oles)24 4418 y(at)c Fs(E)h Fv(=)25 b Fs(E)395 4432 y Fo(n)442 4418 y Fv(,)30 b(where)g Fs(E)827 4432 y Fo(n)904 4418 y Fv(is)f(de\014ned)g(in)f(\(2.10\).)43 b(Using)29 b(a)i(w)m(ell)e(kno) m(wn)g(form)m(ula)g(for)h(a)g(residue)f(of)h(the)g(\000)24 4531 y(function)1264 4669 y(Res)16 b(\(\000\()p Fs(\025)p Fv(\);)f Fs(\025)26 b Fv(=)f Fr(\000)p Fs(n)p Fv(\))g(=)2145 4608 y(\()p Fr(\000)p Fv(1\))2331 4575 y Fo(n)p 2145 4648 234 4 v 2222 4732 a Fs(n)p Fv(!)2419 4669 y Fs(;)1054 b Fv(\(5.1\))24 4855 y(one)30 b(has)664 4993 y(Res)822 4919 y Fq(\000)864 4993 y Fs(\037)921 4955 y Fo(E)921 5015 y Fp(\006)980 4993 y Fv(\()p Fs(x)p Fv(\);)15 b Fr(\000)p Fs(E)1280 5007 y Fo(n)1328 4919 y Fq(\001)1395 4993 y Fv(=)1563 4931 y Fs(C)1628 4945 y Ft(0)p 1501 4972 229 4 v 1501 4990 a Fr(p)p 1577 4990 153 4 v 66 x Fv(2)p Fs(\031)s(\015)1765 4931 y Fv(\()p Fr(\000)p Fv(1\))1951 4898 y Fo(n)p 1765 4972 234 4 v 1842 5055 a Fs(n)p Fv(!)2023 4912 y Fr(p)p 2099 4912 32 4 v 81 x Fs(i)2161 4931 y Fp(\000)p Fo(n)p Fp(\000)2324 4904 y Fk(1)p 2323 4916 31 3 v 2323 4957 a(2)2383 4993 y Fs(D)2458 5007 y Fo(n)2505 4993 y Fv(\()p Fr(\007)2611 4912 y Fq(p)p 2702 4912 200 4 v 81 x Fr(\000)p Fv(2)p Fs(i\015)6 b(x)p Fv(\))31 b Fs(;)453 b Fv(\(5.2\))1832 5281 y(8)p eop %%Page: 9 9 9 8 bop 24 44 a Fv(and)731 182 y(Res)889 109 y Fq(\000)931 182 y Fs(\021)979 145 y Fo(E)976 205 y Fp(\006)1039 182 y Fv(\()p Fs(x)p Fv(\);)15 b(+)p Fs(E)1339 196 y Fo(n)1387 109 y Fq(\001)1454 182 y Fv(=)1622 121 y Fs(C)1687 135 y Ft(0)p 1560 161 229 4 v 1560 179 a Fr(p)p 1635 179 153 4 v 1635 246 a Fv(2)p Fs(\031)s(\015)1823 121 y Fv(\()p Fr(\000)p Fv(1\))2009 88 y Fo(n)p 1823 161 234 4 v 1900 245 a Fs(n)p Fv(!)2082 102 y Fr(p)p 2158 102 32 4 v 80 x Fs(i)2219 121 y Fo(n)p Ft(+)2327 94 y Fk(1)p 2327 106 31 3 v 2327 147 a(2)2387 182 y Fs(D)2462 196 y Fo(n)2509 182 y Fv(\()p Fr(\007)2615 102 y Fq(p)p 2706 102 129 4 v 80 x Fv(2)p Fs(i\015)6 b(x)p Fv(\))31 b Fs(:)520 b Fv(\(5.3\))24 405 y(Hence,)31 b(using)e(the)i(relation)e([18)q(,)i (19)q(,)f(20)q(]:)1506 372 y Ft(5)796 659 y Fs(D)871 673 y Fo(n)918 659 y Fv(\()p Fs(z)t Fv(\))d(=)e(2)1202 621 y Fp(\000)1267 594 y Fh(n)p 1267 606 39 3 v 1271 647 a Fk(2)1335 659 y Fs(e)1377 621 y Fp(\000)1442 594 y Fh(z)1474 573 y Fk(2)p 1442 606 67 3 v 1460 647 a(4)1537 659 y Fs(H)1613 673 y Fo(n)1675 531 y Fq(\022)1789 597 y Fs(z)p 1752 638 122 4 v 1752 656 a Fr(p)p 1828 656 46 4 v 75 x Fv(2)1883 531 y Fq(\023)1995 659 y Fs(;)282 b(n)25 b Fv(=)g(0)p Fs(;)15 b Fv(1)p Fs(;)g Fv(2)p Fs(;)g(:)g(:)g(:)49 b(;)586 b Fv(\(5.4\))24 908 y(together)31 b(with)1374 1021 y Fs(H)1450 1035 y Fo(n)1497 1021 y Fv(\()p Fr(\000)p Fs(z)t Fv(\))26 b(=)f(\()p Fr(\000)p Fv(1\))1992 983 y Fo(n)2039 1021 y Fs(H)2115 1035 y Fo(n)2162 1021 y Fv(\()p Fs(z)t Fv(\))31 b Fs(;)1164 b Fv(\(5.5\))24 1188 y(one)30 b(obtains)1292 1301 y(Res)1450 1227 y Fq(\000)1492 1301 y Fs(\037)1549 1263 y Fo(E)1549 1323 y Fp(\006)1609 1301 y Fv(\()p Fs(x)p Fv(\);)15 b Fr(\000)p Fs(E)1909 1315 y Fo(n)1956 1227 y Fq(\001)2039 1301 y Fr(\030)40 b Fg(f)2180 1263 y Ft(+)2180 1323 y Fo(n)2238 1301 y Fv(\()p Fs(x)p Fv(\))31 b Fs(;)1082 b Fv(\(5.6\))24 1468 y(and)1296 1581 y(Res)1455 1507 y Fq(\000)1496 1581 y Fs(\021)1544 1543 y Fo(E)1541 1603 y Fp(\006)1604 1581 y Fv(\()p Fs(x)p Fv(\);)15 b(+)p Fs(E)1904 1595 y Fo(n)1952 1507 y Fq(\001)2034 1581 y Fr(\030)40 b Fg(f)2175 1543 y Fp(\000)2175 1603 y Fo(n)2234 1581 y Fv(\()p Fs(x)p Fv(\))31 b Fs(:)1086 b Fv(\(5.7\))24 1747 y(No)m(w,)39 b(it)d(is)f(natural)h(to)h(in)m(tro)s(duce)f(t)m(w)m(o)i(Hardy)e (classes)h(of)f(functions)f([21)r(].)59 b(Recall,)38 b(that)f(a)g(smo)s(oth)24 1860 y(function)20 b Fs(f)35 b Fv(=)24 b Fs(f)10 b Fv(\()p Fs(E)5 b Fv(\))22 b(is)f(in)f(the)i (Hardy)g(class)f(from)g(ab)s(o)m(v)m(e)i Fr(H)2100 1827 y Ft(2)2099 1883 y(+)2180 1860 y Fv(\(from)e(b)s(elo)m(w)g Fr(H)2748 1827 y Ft(2)2747 1883 y Fp(\000)2806 1860 y Fv(\))h(if)e Fs(f)10 b Fv(\()p Fs(E)5 b Fv(\))22 b(is)f(a)h(b)s (oundary)24 1973 y(v)-5 b(alue)30 b(of)h(an)f(analytic)h(function)e(in) g(the)i(upp)s(er,)e(i.e.)42 b(Im)15 b Fs(E)31 b Fr(\025)25 b Fv(0)31 b(\(lo)m(w)m(er,)h(i.e.)42 b(Im)14 b Fs(E)32 b Fr(\024)25 b Fv(0\))32 b(half)d(complex)24 2086 y Fs(E)5 b Fv(-plane)39 b(v)-5 b(anishing)37 b(faster)i(than)g(an)m(y)h(p)s(o)m (w)m(er)f(of)h Fs(E)k Fv(at)d(the)e(upp)s(er)e(\(lo)m(w)m(er\))k (semi-circle)d Fr(j)p Fs(E)5 b Fr(j)41 b(!)f(1)p Fv(.)24 2199 y(De\014ne)945 2312 y(\010)1011 2326 y Fp(\000)1095 2312 y Fv(:=)1216 2211 y Fq(n)1277 2312 y Fs(\036)25 b Fr(2)g(S)7 b Fv(\()p Fn(R)1599 2326 y Fo(x)1649 2312 y Fv(\))1699 2207 y Fq(\014)1699 2262 y(\014)1699 2317 y(\014)1745 2312 y Fs(f)j Fv(\()p Fs(E)5 b Fv(\))25 b(:=)h Fr(h)15 b Fs(\037)2196 2274 y Fo(E)2196 2334 y Fp(\006)2256 2312 y Fr(j)p Fs(\036)g Fr(i)26 b(2)f(H)2575 2274 y Ft(2)2574 2334 y Fp(\000)2648 2211 y Fq(o)2738 2312 y Fs(;)735 b Fv(\(5.8\))24 2496 y(and)949 2609 y(\010)1015 2623 y Ft(+)1099 2609 y Fv(:=)1220 2508 y Fq(n)1281 2609 y Fs(\036)25 b Fr(2)g(S)7 b Fv(\()p Fn(R)1603 2623 y Fo(x)1653 2609 y Fv(\))1703 2505 y Fq(\014)1703 2559 y(\014)1703 2614 y(\014)1749 2609 y Fs(f)j Fv(\()p Fs(E)5 b Fv(\))26 b(:=)f Fr(h)15 b Fs(\021)2191 2572 y Fo(E)2188 2632 y Fp(\006)2251 2609 y Fr(j)p Fs(\036)g Fr(i)26 b(2)f(H)2570 2572 y Ft(2)2569 2632 y(+)2643 2508 y Fq(o)2734 2609 y Fs(:)739 b Fv(\(5.9\))24 2811 y(It)30 b(is)g(eviden)m(t)g(from)g (\(4.26\))i(that)f(\010)1272 2825 y Ft(+)1356 2811 y Fv(=)p 1452 2738 125 4 v 25 w(\010)1518 2825 y Fp(\000)1577 2811 y Fv(,)f(that)h(is)1570 3015 y(\010)1636 3029 y Ft(+)1719 3015 y Fv(=)25 b Fw(T)p Fv(\(\010)1989 3029 y Fp(\000)2048 3015 y Fv(\))31 b Fs(:)1314 b Fv(\(5.10\))24 3219 y(Due)30 b(to)g(the)g(Gel'fand-Maurin)e(sp)s(ectral)h(theorem)h ([22)q(,)g(23)q(])g(an)m(y)g(function)e Fs(\036)2758 3186 y Fp(\000)2843 3219 y Fr(2)d Fv(\010)2995 3233 y Fp(\000)3083 3219 y Fv(ma)m(y)30 b(b)s(e)f(decom-)24 3332 y(p)s(osed)g(with)g(resp)s(ect)i(to)g Fs(\037)966 3299 y Fo(E)966 3355 y Fp(\006)1056 3332 y Fv(family)1112 3587 y Fs(\036)1166 3550 y Fp(\000)1225 3587 y Fv(\()p Fs(x)p Fv(\))26 b(=)1469 3501 y Fq(X)1507 3693 y Fp(\006)1616 3464 y Fq(Z)1707 3490 y Fp(1)1666 3670 y(\0001)1811 3587 y Fs(dE)21 b(\037)2003 3550 y Fo(E)2003 3610 y Fp(\006)2062 3587 y Fv(\()p Fs(x)p Fv(\))p Fr(h)15 b Fs(\037)2291 3550 y Fo(E)2291 3610 y Fp(\006)2352 3587 y Fr(j)p Fs(\036)2431 3550 y Fp(\000)2506 3587 y Fr(i)30 b Fs(;)857 b Fv(\(5.11\))24 3887 y(and)29 b(an)m(y)i(function)e Fs(\036)782 3854 y Ft(+)867 3887 y Fr(2)24 b Fv(\010)1018 3901 y Ft(+)1107 3887 y Fv(ma)m(y)31 b(b)s(e)f(decomp)s(osed)g(with)f(resp)s(ect)i(to)g Fs(\021)2614 3854 y Fo(E)2611 3909 y Fp(\006)2704 3887 y Fv(family)1121 4142 y Fs(\036)1175 4104 y Ft(+)1234 4142 y Fv(\()p Fs(x)p Fv(\))26 b(=)1478 4055 y Fq(X)1516 4247 y Fp(\006)1624 4018 y Fq(Z)1715 4044 y Fp(1)1675 4224 y(\0001)1819 4142 y Fs(dE)21 b(\021)2002 4104 y Fo(E)1999 4164 y Fp(\006)2062 4142 y Fv(\()p Fs(x)p Fv(\))p Fr(h)15 b Fs(\021)2282 4104 y Fo(E)2279 4164 y Fp(\006)2343 4142 y Fr(j)p Fs(\036)2422 4104 y Ft(+)2497 4142 y Fr(i)31 b Fs(:)865 b Fv(\(5.12\))24 4426 y(Applying)28 b(the)i(Residue)f (Theorem)h(one)h(easily)f(pro)m(v)m(es)h(the)f(follo)m(wing)p 24 4505 1465 4 v 127 4559 a Fk(5)162 4590 y Fj(In)25 b([18)q(])h(the)f(corresp)r(onding)i(equation)e(9.253)j(has)e(a)g (wrong)g(sign.)1832 5281 y Fv(9)p eop %%Page: 10 10 10 9 bop 24 44 a Fw(Theorem)34 b(1)45 b Ff(F)-7 b(or)34 b(any)f(function)g Fs(\036)1321 11 y Fp(\006)1405 44 y Fr(2)25 b Fv(\010)1557 58 y Fp(\006)1649 44 y Ff(one)32 b(has)1220 300 y Fs(\036)1274 262 y Fp(\000)1333 300 y Fv(\()p Fs(x)p Fv(\))26 b(=)1608 186 y Fp(1)1578 213 y Fq(X)1577 408 y Fo(n)p Ft(=0)1725 300 y Fg(f)1755 262 y Fp(\000)1755 322 y Fo(n)1814 300 y Fv(\()p Fs(x)p Fv(\))p Fr(h)15 b Fg(f)2016 262 y Ft(+)2016 322 y Fo(n)2076 300 y Fr(j)p Fs(\036)2155 262 y Fp(\000)2229 300 y Fr(i)33 b Fs(;)1131 b Fv(\(5.13\))24 564 y Ff(and)1220 799 y Fs(\036)1274 761 y Ft(+)1333 799 y Fv(\()p Fs(x)p Fv(\))26 b(=)1608 685 y Fp(1)1578 712 y Fq(X)1577 907 y Fo(n)p Ft(=0)1725 799 y Fg(f)1755 761 y Ft(+)1755 821 y Fo(n)1814 799 y Fv(\()p Fs(x)p Fv(\))p Fr(h)15 b Fg(f)2016 761 y Fp(\000)2016 821 y Fo(n)2076 799 y Fr(j)p Fs(\036)2155 761 y Ft(+)2229 799 y Fr(i)33 b Fs(:)1131 b Fv(\(5.14\))24 1076 y(The)36 b(pro)s(of)h(go)s(es)h(along)f(the)h(same)f(lines)f(as)i (the)f(corresp)s(onding)e(pro)s(of)i(of)g(Theorem)g(2)h(in)e([1)q(].)61 b(The)24 1189 y(ab)s(o)m(v)m(e)31 b(theorem)g(implies)d(the)i(follo)m (wing)f(sp)s(ectral)h(resolutions)e(of)j(the)g(Hamiltonian:)880 1418 y Fq(b)859 1441 y Fs(H)h Fv(=)1063 1355 y Fq(X)1101 1547 y Fp(\006)1209 1318 y Fq(Z)1300 1344 y Fp(1)1260 1524 y(\0001)1405 1441 y Fs(dE)20 b(E)5 b Fr(j)p Fs(\037)1693 1404 y Fo(E)1693 1464 y Fp(\006)1769 1441 y Fr(ih)15 b Fs(\037)1911 1404 y Fo(E)1911 1464 y Fp(\006)1971 1441 y Fr(j)25 b Fv(=)g Fr(\000)2234 1328 y Fp(1)2204 1355 y Fq(X)2203 1549 y Fo(n)p Ft(=0)2351 1441 y Fs(E)2418 1455 y Fo(n)2466 1441 y Fr(j)p Fg(f)2521 1404 y Fp(\000)2521 1464 y Fo(n)2595 1441 y Fr(ih)15 b Fg(f)2710 1404 y Ft(+)2710 1464 y Fo(n)2769 1441 y Fr(j)31 b Fs(;)603 b Fv(\(5.15\))24 1709 y(on)30 b(\010)216 1723 y Fp(\000)275 1709 y Fv(,)g(and)931 1867 y Fq(b)910 1890 y Fs(H)i Fv(=)1114 1803 y Fq(X)1152 1995 y Fp(\006)1261 1766 y Fq(Z)1352 1792 y Fp(1)1311 1972 y(\0001)1456 1890 y Fs(dE)21 b(E)5 b Fr(j)p Fs(\021)1736 1852 y Fo(E)1733 1912 y Fp(\006)1812 1890 y Fr(ih)15 b Fs(\021)1945 1852 y Fo(E)1942 1912 y Fp(\006)2005 1890 y Fr(j)26 b Fv(=)2183 1776 y Fp(1)2153 1803 y Fq(X)2152 1998 y Fo(n)p Ft(=0)2300 1890 y Fs(E)2367 1904 y Fo(n)2414 1890 y Fr(j)p Fg(f)2469 1852 y Ft(+)2469 1912 y Fo(n)2543 1890 y Fr(ih)15 b Fg(f)2658 1852 y Fp(\000)2658 1912 y Fo(n)2718 1890 y Fr(j)30 b Fs(;)655 b Fv(\(5.16\))24 2128 y(on)30 b(\010)216 2142 y Ft(+)275 2128 y Fv(.)40 b(The)30 b(same)h(tec)m(hniques)f(ma)m(y)h(b)s(e)f(applied)e(for)i(the) g(resolv)m(en)m(t)i(op)s(erator)1481 2353 y Fs(R)q Fv(\()p Fs(z)t(;)1694 2330 y Fq(b)1672 2353 y Fs(H)7 b Fv(\))26 b(=)2019 2291 y(1)p 1922 2332 241 4 v 1943 2408 a Fq(b)1922 2431 y Fs(H)h Fr(\000)20 b Fs(z)2203 2353 y(:)1225 b Fv(\(5.17\))24 2586 y(One)30 b(obtains)597 2821 y Fs(R)q Fv(\()p Fs(z)t(;)810 2798 y Fq(b)788 2821 y Fs(H)8 b Fv(\))26 b(=)1029 2734 y Fq(X)1067 2926 y Fp(\006)1175 2697 y Fq(Z)1266 2723 y Fp(1)1226 2903 y(\0001)1451 2759 y Fs(dE)p 1395 2800 230 4 v 1395 2883 a(E)g Fr(\000)20 b Fs(z)1650 2821 y Fr(j)p Fs(\037)1732 2783 y Fo(E)1732 2843 y Fp(\006)1807 2821 y Fr(ih)15 b Fs(\037)1949 2783 y Fo(E)1949 2843 y Fp(\006)2010 2821 y Fr(j)40 b Fv(=)2218 2707 y Fp(1)2187 2734 y Fq(X)2186 2929 y Fo(n)p Ft(=0)2508 2759 y Fv(1)p 2360 2800 343 4 v 2360 2883 a Fr(\000)p Fs(E)2498 2897 y Fo(n)2565 2883 y Fr(\000)19 b Fs(z)2727 2821 y Fr(j)p Fg(f)2782 2783 y Fp(\000)2782 2843 y Fo(n)2856 2821 y Fr(ih)c Fg(f)2971 2783 y Ft(+)2971 2843 y Fo(n)3031 2821 y Fr(j)30 b Fs(;)342 b Fv(\(5.18\))24 3089 y(on)30 b(\010)216 3103 y Fp(\000)275 3089 y Fv(,)g(and)641 3344 y Fs(R)q Fv(\()p Fs(z)t(;)854 3321 y Fq(b)832 3344 y Fs(H)8 b Fv(\))26 b(=)1072 3258 y Fq(X)1111 3450 y Fp(\006)1219 3221 y Fq(Z)1310 3247 y Fp(1)1269 3427 y(\0001)1494 3283 y Fs(dE)p 1439 3323 230 4 v 1439 3407 a(E)g Fr(\000)20 b Fs(z)1694 3344 y Fr(j)p Fs(\021)1767 3307 y Fo(E)1764 3367 y Fp(\006)1843 3344 y Fr(ih)15 b Fs(\021)1976 3307 y Fo(E)1973 3367 y Fp(\006)2036 3344 y Fr(j)41 b Fv(=)2244 3231 y Fp(1)2214 3258 y Fq(X)2213 3452 y Fo(n)p Ft(=0)2499 3283 y Fv(1)p 2386 3323 272 4 v 2386 3407 a Fs(E)2453 3421 y Fo(n)2521 3407 y Fr(\000)20 b Fs(z)2683 3344 y Fr(j)p Fg(f)2738 3307 y Ft(+)2738 3367 y Fo(n)2812 3344 y Fr(ih)15 b Fg(f)2927 3307 y Fp(\000)2927 3367 y Fo(n)2987 3344 y Fr(j)30 b Fs(;)386 b Fv(\(5.19\))24 3638 y(on)39 b(\010)225 3652 y Ft(+)284 3638 y Fv(.)69 b(Hence,)43 b Fs(R)q Fv(\()p Fs(z)t(;)898 3615 y Fq(b)876 3638 y Fs(H)7 b Fv(\))p Fr(j)1019 3652 y Ft(\010)1070 3661 y Fl(\000)1167 3638 y Fv(has)39 b(p)s(oles)g(at)h Fs(z)45 b Fv(=)c Fr(\000)p Fs(E)2035 3652 y Fo(n)2082 3638 y Fv(,)h(and)d Fs(R)q Fv(\()p Fs(z)t(;)2548 3615 y Fq(b)2526 3638 y Fs(H)8 b Fv(\))p Fr(j)2670 3652 y Ft(\010)2721 3661 y Fk(+)2816 3638 y Fv(has)39 b(p)s(oles)g(at)h Fs(z)45 b Fv(=)c Fs(E)3613 3652 y Fo(n)3660 3638 y Fv(.)24 3751 y(As)c(usual)f(eigen)m(v)m(ectors)j Fg(f)955 3718 y Fp(\000)955 3773 y Fo(n)1051 3751 y Fv(and)e Fg(f)1265 3718 y Ft(+)1265 3773 y Fo(n)1361 3751 y Fv(corresp)s(onding)e(to)j(p)s(oles)e(of)i(the) f(resolv)m(en)m(t)h(are)g(in)m(terpreted)f(as)24 3864 y(resonan)m(t)31 b(states.)41 b(Note,)32 b(that)1081 4089 y Fr(\000)1204 4027 y Fv(1)p 1162 4068 132 4 v 1162 4151 a(2)p Fs(\031)s(i)1318 3965 y Fq(I)1369 4171 y Fo(\015)1405 4179 y Fh(n)1467 4089 y Fs(R)q Fv(\()p Fs(z)t(;)1680 4066 y Fq(b)1658 4089 y Fs(H)8 b Fv(\))p Fs(dz)30 b Fv(=)25 b Fr(j)p Fg(f)2047 4051 y Ft(+)2047 4111 y Fo(n)2121 4089 y Fr(ih)15 b Fg(f)2236 4051 y Fp(\000)2236 4111 y Fo(n)2295 4089 y Fr(j)26 b Fv(:=)2485 4066 y Fq(b)2467 4089 y Fs(P)2525 4103 y Fo(n)2603 4089 y Fs(;)825 b Fv(\(5.20\))24 4331 y(where)30 b Fs(\015)334 4345 y Fo(n)411 4331 y Fv(is)f(a)i(closed)f(curv)m(e)h(that)g(encircles)e(the)i(singularit)m (y)d Fs(z)i Fv(=)25 b Fs(E)2492 4345 y Fo(n)2539 4331 y Fv(.)40 b(Clearly)-8 b(,)1508 4496 y Fq(b)1490 4519 y Fs(P)1548 4533 y Fo(n)1616 4519 y Fr(\001)1679 4496 y Fq(b)1661 4519 y Fs(P)1719 4533 y Fo(m)1812 4519 y Fv(=)25 b Fs(\016)1948 4533 y Fo(nm)2075 4496 y Fq(b)2057 4519 y Fs(P)2115 4533 y Fo(n)2193 4519 y Fs(;)1235 b Fv(\(5.21\))24 4708 y(and)29 b(the)i(sp)s(ectral)f(decomp)s(osition)f (of)1422 4685 y Fq(b)1401 4708 y Fs(H)37 b Fv(ma)m(y)31 b(b)s(e)f(written)g(as)g(follo)m(ws:)1259 4937 y Fq(b)1238 4960 y Fs(H)i Fv(=)1473 4847 y Fp(1)1443 4874 y Fq(X)1442 5068 y Fo(n)p Ft(=0)1605 4960 y Fs(E)1672 4974 y Fo(n)1737 4937 y Fq(b)1719 4960 y Fs(P)1777 4974 y Fo(n)1850 4960 y Fv(=)25 b Fr(\000)2063 4847 y Fp(1)2032 4874 y Fq(X)2032 5068 y Fo(n)p Ft(=0)2195 4960 y Fs(E)2262 4974 y Fo(n)2327 4937 y Fq(b)2309 4960 y Fs(P)2380 4923 y Fp(y)2367 4983 y Fo(n)2446 4960 y Fs(:)982 b Fv(\(5.22\))1809 5281 y(10)p eop %%Page: 11 11 11 10 bop 165 51 a Fv(Finally)-8 b(,)39 b(let)g(us)f(note,)j(that)f (restriction)d(of)i(the)g(unitary)f(group)g Fs(U)10 b Fv(\()p Fs(t)p Fv(\))39 b(=)g Fs(e)2892 18 y Fp(\000)p Fo(i)2987 1 y Fm(b)2971 18 y Fo(H)5 b(t)3103 51 y Fv(de\014ned)37 b(on)i(the)24 164 y(Hilb)s(ert)28 b(space)j Fs(L)642 131 y Ft(2)681 164 y Fv(\()p Fn(R)s Fv(\))37 b(to)31 b(\010)1025 178 y Fp(\006)1114 164 y Fv(no)f(longer)g(de\014nes)g(a)h (group.)40 b(It)30 b(giv)m(es)h(rise)e(to)i(t)m(w)m(o)h(semigroups:) 1067 368 y Fs(U)1129 382 y Fp(\000)1188 368 y Fv(\()p Fs(t)p Fv(\))56 b(:)g(\010)1494 382 y Fp(\000)1608 368 y Fr(\000)-16 b(!)56 b Fv(\010)1876 382 y Fp(\000)1965 368 y Fs(;)197 b Fv(for)91 b Fs(t)25 b Fr(\025)g Fv(0)31 b Fs(;)811 b Fv(\(5.23\))24 572 y(and)1067 685 y Fs(U)1129 699 y Ft(+)1188 685 y Fv(\()p Fs(t)p Fv(\))56 b(:)g(\010)1494 699 y Ft(+)1608 685 y Fr(\000)-16 b(!)56 b Fv(\010)1876 699 y Ft(+)1965 685 y Fs(;)197 b Fv(for)91 b Fs(t)25 b Fr(\024)g Fv(0)31 b Fs(:)811 b Fv(\(5.24\))24 852 y(Using)29 b(\(5.15\),)k(\(5.16\))g(and)c(the)i(form)m(ula)f(for)g Fs(E)1703 866 y Fo(n)1775 852 y Fv(=)25 b Fs(i\015)5 b Fv(\()p Fs(n)21 b Fv(+)2165 816 y Ft(1)p 2165 831 36 4 v 2165 883 a(2)2211 852 y Fv(\))30 b(one)h(\014nds:)968 1134 y Fs(\036)1022 1097 y Fp(\000)1082 1134 y Fv(\()p Fs(t)p Fv(\))25 b(=)g Fs(U)1368 1148 y Fp(\000)1428 1134 y Fv(\()p Fs(t)p Fv(\))p Fs(\036)1585 1097 y Fp(\000)1670 1134 y Fv(=)1797 1020 y Fp(1)1766 1048 y Fq(X)1765 1242 y Fo(n)p Ft(=0)1914 1134 y Fs(e)1956 1097 y Fp(\000)p Fo(\015)t Ft(\()p Fo(n)p Ft(+)2186 1069 y Fk(1)p 2186 1081 31 3 v 2186 1123 a(2)2227 1097 y Ft(\))p Fo(t)2317 1111 y Fq(b)2299 1134 y Fs(P)2370 1097 y Fp(y)2357 1157 y Fo(n)2405 1134 y Fs(\036)2459 1097 y Fp(\000)2549 1134 y Fs(;)879 b Fv(\(5.25\))24 1414 y(for)30 b Fs(t)25 b Fr(\025)g Fv(0,)31 b(and)997 1682 y Fs(\036)1051 1645 y Ft(+)1110 1682 y Fv(\()p Fs(t)p Fv(\))26 b(=)e Fs(U)1396 1696 y Ft(+)1456 1682 y Fv(\()p Fs(t)p Fv(\))p Fs(\036)1613 1645 y Ft(+)1698 1682 y Fv(=)1825 1569 y Fp(1)1794 1596 y Fq(X)1794 1790 y Fo(n)p Ft(=0)1942 1682 y Fs(e)1984 1645 y Fo(\015)t Ft(\()p Fo(n)p Ft(+)2159 1618 y Fk(1)p 2159 1630 V 2159 1671 a(2)2200 1645 y Ft(\))p Fo(t)2290 1660 y Fq(b)2272 1682 y Fs(P)2330 1696 y Fo(n)2377 1682 y Fs(\036)2431 1645 y Ft(+)2521 1682 y Fs(;)907 b Fv(\(5.26\))24 1978 y(for)36 b Fs(t)f Fr(\024)g Fv(0.)59 b(W)-8 b(e)37 b(stress)g(that)g Fs(\036)1147 1939 y Fp(\000)1147 2002 y Fo(t)1242 1978 y Fv(\()p Fs(\036)1331 1939 y Ft(+)1331 2002 y Fo(t)1391 1978 y Fv(\))f(do)s(es)g(b)s(elong)g(to)h Fs(L)2149 1945 y Ft(2)2188 1978 y Fv(\()p Fn(R)s Fv(\))43 b(also)36 b(for)g Fs(t)f(<)g Fv(0)i(\()p Fs(t)e(>)g Fv(0\).)60 b(Ho)m(w)m(ev)m(er,)24 2090 y Fs(\036)78 2052 y Fp(\000)78 2115 y Fo(t)164 2090 y Fr(2)26 b Fv(\010)317 2104 y Fp(\000)407 2090 y Fv(\()p Fs(\036)496 2052 y Ft(+)496 2115 y Fo(t)583 2090 y Fr(2)h Fv(\010)737 2104 y Ft(+)795 2090 y Fv(\))32 b(only)e(for)i Fs(t)26 b Fr(\025)h Fv(0)32 b(\()p Fs(t)27 b Fr(\024)g Fv(0\).)44 b(This)30 b(w)m(a)m(y)i(the)g(irrev)m(ersibilit) m(y)c(en)m(ters)k(the)f(dynamics)24 2203 y(of)f(the)h(rev)m(ersed)f (oscillator)g(b)m(y)g(restricting)g(it)f(to)j(the)e(dense)g(subspace)g (\010)2642 2217 y Fp(\006)2731 2203 y Fv(of)g Fs(L)2896 2170 y Ft(2)2936 2203 y Fv(\()p Fn(R)s Fv(\).)24 2490 y Fu(6)134 b(Scattering)46 b(vs.)60 b(resonan)l(t)46 b(states)24 2693 y Fv(T)-8 b(o)32 b(compare)h(the)f(ph)m(ysical)e(prop) s(erties)h(of)h(energy)g(eigenstates)h Fs(\037)2379 2660 y Fo(E)2379 2715 y Fp(\006)2471 2693 y Fv(and)e Fs(\021)2697 2660 y Fo(E)2694 2715 y Fp(\006)2789 2693 y Fv(and)h(resonan)m(t)g (states)h Fg(f)3626 2660 y Fp(\006)3626 2715 y Fo(n)24 2806 y Fv(let)28 b(us)g(in)m(v)m(estigate)h(its)f(asymptotic)h(b)s(eha) m(vior)e(at)i Fs(x)c Fr(\000)-15 b(!)25 b(\0061)p Fv(.)40 b(F)-8 b(ollo)m(wing)28 b([20)q(])g(\(see)i(also)e([10)q(,)h(11)q(]\))g (one)24 2919 y(\014nds)213 2886 y Ft(6)523 3077 y Fs(\037)580 3039 y Fo(E)580 3099 y Fp(\000)639 3077 y Fv(\()p Fs(x)d Fr(!)f Fv(+)p Fr(1)p Fv(\))40 b Fr(\030)1217 2934 y Fq(r)p 1308 2934 72 4 v 1321 3015 a Fv(1)p 1318 3056 52 4 v 1318 3139 a Fs(x)1410 3077 y Fv(exp)1564 2949 y Fq(\024)1612 3077 y Fs(i)1658 2949 y Fq(\022)1735 3015 y Fs(\015)p 1735 3056 53 4 v 1738 3139 a Fv(2)1797 3077 y Fs(x)1849 3039 y Ft(2)1909 3077 y Fv(+)2010 3015 y Fs(E)p 2010 3056 73 4 v 2020 3139 a(\015)2107 3077 y Fv(log)q(\()2259 2997 y Fq(p)p 2351 2997 98 4 v 2351 3077 a Fv(2)p Fs(\015)5 b(x)p Fv(\))21 b(+)2657 3015 y Fs(\031)p 2657 3056 56 4 v 2662 3139 a Fv(4)2732 3015 y Fs(E)p 2732 3056 73 4 v 2742 3139 a(\015)2834 3077 y Fv(+)2935 3015 y Fs(\031)p 2935 3056 56 4 v 2940 3139 a Fv(8)3000 2949 y Fq(\023\025)3161 3077 y Fs(;)312 b Fv(\(6.1\))24 3289 y(and)57 3538 y Fs(\037)114 3501 y Fo(E)114 3561 y Fp(\000)173 3538 y Fv(\()p Fs(x)26 b Fr(!)f(\0001)p Fv(\))83 b Fr(\030)f Fs(i)866 3396 y Fq(r)p 958 3396 72 4 v 971 3477 a Fv(1)p 968 3518 52 4 v 968 3601 a Fs(x)1045 3410 y Fq(\032)1113 3438 y(\020)1167 3538 y Fv(1)21 b(+)f Fs(e)1366 3493 y Fp(\000)p Ft(2)p Fo(\031)1509 3466 y Fh(E)p 1509 3478 48 3 v 1515 3519 a(\015)1571 3438 y Fq(\021)1640 3538 y Fv(exp)1794 3410 y Fq(\024)1842 3538 y Fr(\000)p Fs(i)1959 3410 y Fq(\022)2036 3477 y Fs(\015)p 2036 3518 53 4 v 2039 3601 a Fv(2)2098 3538 y Fs(x)2150 3501 y Ft(2)2210 3538 y Fv(+)2311 3477 y Fs(E)p 2311 3518 73 4 v 2321 3601 a(\015)2408 3538 y Fv(log)r(\()2561 3459 y Fq(p)p 2652 3459 98 4 v 79 x Fv(2)p Fs(\015)6 b(x)p Fv(\))20 b Fr(\000)2958 3477 y Fs(\031)p 2958 3518 56 4 v 2963 3601 a Fv(4)3033 3477 y Fs(E)p 3033 3518 73 4 v 3043 3601 a(\015)3135 3538 y Fv(+)3236 3477 y(3)p Fs(\031)p 3236 3518 101 4 v 3264 3601 a Fv(8)3367 3538 y(+)g Fs(\036)3512 3410 y Fq(\023\025)682 3790 y Fr(\000)92 b Fs(e)887 3744 y Fp(\000)p Fo(\031)996 3717 y Fh(E)p 996 3729 48 3 v 1002 3770 a(\015)1072 3790 y Fv(exp)1226 3662 y Fq(\024)1274 3790 y Fs(i)1320 3662 y Fq(\022)1398 3728 y Fs(\015)p 1398 3769 53 4 v 1401 3852 a Fv(2)1460 3790 y Fs(x)1512 3752 y Ft(2)1571 3790 y Fr(\000)1672 3728 y Fs(E)p 1672 3769 73 4 v 1682 3852 a(\015)1770 3790 y Fv(log)q(\()1922 3710 y Fq(p)p 2013 3710 98 4 v 80 x Fv(2)p Fs(\015)6 b(x)p Fv(\))20 b Fr(\000)2319 3728 y Fs(\031)p 2319 3769 56 4 v 2324 3852 a Fv(4)2394 3728 y Fs(E)p 2394 3769 73 4 v 2404 3852 a(\015)2497 3790 y Fv(+)2598 3728 y Fs(\031)p 2598 3769 56 4 v 2603 3852 a Fv(8)2663 3662 y Fq(\023\025\033)2891 3790 y Fs(;)582 b Fv(\(6.2\))24 4057 y(where)37 b Fs(\036)h Fv(=)f(arg)17 b(\000\()p Fr(\000)p Fs(i)841 4021 y Fo(E)p 841 4036 V 849 4088 a(\015)932 4057 y Fv(+)1038 4021 y Ft(1)p 1038 4036 36 4 v 1038 4088 a(2)1083 4057 y Fv(\))38 b(=)g(\000\()p Fs(\027)31 b Fv(+)24 b(1\).)64 b(Hence)39 b(energy)f(eigenstates)h Fs(\037)2798 4024 y Fo(E)2798 4080 y Fp(\000)2895 4057 y Fv(represen)m(t)f(scattering)24 4188 y(states)29 b(\(see)g([10)q(])f (for)g(more)h(details\).)39 b(The)27 b(same)i(is)e(true)h(for)g Fs(\037)2233 4155 y Fo(E)2233 4210 y Ft(+)2320 4188 y Fv(and)g Fs(\021)2543 4155 y Fo(E)2540 4210 y Fp(\006)2603 4188 y Fv(.)40 b(In)27 b(particular)f(one)j(\014nds)d(for)p 24 4279 1465 4 v 127 4333 a Fk(6)162 4364 y Fj(Putting)f Fi(a)d Fj(=)f Fc(\000)p Fi(E)t(=\015)29 b Fj(in)d(equation)f(19.17.9)j (in)e([20)q(])g(and)f(using)h(relation)h(19.3.1)1486 4522 y Fi(U)8 b Fj(\()p Fi(a;)13 b(x)p Fj(\))21 b(=)g Fi(D)1890 4543 y Fl(\000)p Fh(a)p Fl(\000)2030 4523 y Fa(1)p 2030 4531 29 3 v 2030 4564 a(2)2072 4522 y Fj(\()p Fi(x)p Fj(\))k Fi(;)24 4691 y Fj(one)g(\014nds:)933 4807 y Fi(U)1006 4702 y Fd(\022)1062 4807 y Fc(\000)p Fi(i)1158 4759 y(E)p 1158 4790 61 4 v 1166 4858 a(\015)1229 4807 y(;)1263 4742 y Fd(p)p 1340 4742 83 4 v 65 x Fj(2)p Fi(\015)t(xe)1502 4771 y Fl(\000)1560 4752 y Fa(1)p 1560 4760 29 3 v 1560 4793 a(4)1598 4771 y Fh(i\031)1662 4702 y Fd(\023)1740 4807 y Fj(=)c Fi(D)1884 4815 y Fl(\000)p Fh(\027)s Fl(\000)p Fk(1)2049 4807 y Fj(\()2079 4741 y Fd(p)p 2156 4741 169 4 v 66 x Fc(\000)p Fj(2)p Fi(i\015)t(x)p Fj(\))34 b Fc(\030)g Fi(\037)2574 4771 y Fh(E)2574 4820 y Fl(\000)2626 4807 y Fj(\()p Fi(x)p Fj(\))25 b Fi(:)1809 5281 y Fv(11)p eop %%Page: 12 12 12 11 bop 24 44 a Fv(the)30 b(re\015ection)g(and)g(transmission)e (amplitudes)g Fs(R)j Fv(and)f Fs(T)43 b Fv(for)30 b Fs(\037)2312 11 y Fo(E)2312 67 y Fp(\006)2402 44 y Fv(scattering)h(states)h([8,)f (10)q(]:)1060 293 y Fs(R)q Fv(\()p Fs(\037)1222 256 y Fo(E)1222 316 y Fp(\006)1281 293 y Fv(\))84 b(=)e Fr(\000)1706 232 y Fs(i)p 1634 273 177 4 v 1634 291 a Fr(p)p 1710 291 101 4 v 75 x Fv(2)p Fs(\031)1835 293 y(e)1877 248 y Fp(\000)1942 221 y Fh(\031)r(E)p 1943 233 86 3 v 1952 274 a Fk(2)p Fh(\015)2057 293 y Fv(\000)2129 165 y Fq(\022)2206 232 y Fv(1)p 2206 273 46 4 v 2206 356 a(2)2282 293 y Fr(\000)20 b Fs(i)2414 232 y(E)p 2414 273 73 4 v 2424 356 a(\015)2496 165 y Fq(\023)2609 293 y Fs(;)864 b Fv(\(6.3\))1064 545 y Fs(T)13 b Fv(\()p Fs(\037)1222 507 y Fo(E)1222 567 y Fp(\006)1281 545 y Fv(\))84 b(=)1629 483 y(1)p 1563 524 177 4 v 1563 542 a Fr(p)p 1639 542 101 4 v 75 x Fv(2)p Fs(\031)1765 545 y(e)1817 472 y Fh(\031)r(E)p 1817 484 86 3 v 1827 525 a Fk(2)p Fh(\015)1932 545 y Fv(\000)2004 417 y Fq(\022)2081 483 y Fv(1)p 2081 524 46 4 v 2081 607 a(2)2156 545 y Fr(\000)20 b Fs(i)2288 483 y(E)p 2288 524 73 4 v 2298 607 a(\015)2371 417 y Fq(\023)2483 545 y Fs(:)990 b Fv(\(6.4\))24 798 y(Clearly)-8 b(,)29 b(computing)h Fs(R)h Fv(and)f Fs(T)43 b Fv(for)30 b(time-rev)m(ersed)g Fs(\021)1928 765 y Fo(E)1925 820 y Fp(\006)2019 798 y Fv(scattering)h(states)g(one)g(\014nds:)1051 1010 y Fs(R)q Fv(\()p Fs(\021)1204 972 y Fo(E)1201 1032 y Fp(\006)1264 1010 y Fv(\))25 b(=)p 1420 922 257 4 v 25 w Fs(R)q Fv(\()p Fs(\037)1582 979 y Fo(E)1582 1033 y Fp(\006)1642 1010 y Fv(\))30 b Fs(;)252 b(T)13 b Fv(\()p Fs(\021)2133 972 y Fo(E)2130 1032 y Fp(\006)2193 1010 y Fv(\))26 b(=)p 2350 922 253 4 v 25 w Fs(T)13 b Fv(\()p Fs(\037)2508 979 y Fo(E)2508 1033 y Fp(\006)2567 1010 y Fv(\))31 b Fs(:)840 b Fv(\(6.5\))24 1203 y(Note,)32 b(that)f Fs(R)q Fv(\()p Fs(\037)628 1170 y Fo(E)628 1225 y Fp(\006)688 1203 y Fv(\))f(and)g Fs(T)13 b Fv(\()p Fs(\037)1088 1170 y Fo(E)1088 1225 y Fp(\006)1148 1203 y Fv(\))31 b(ha)m(v)m(e)h(p)s(oles)d(at)i Fs(E)g Fv(=)25 b Fr(\000)p Fs(E)2097 1217 y Fo(n)2144 1203 y Fv(,)31 b(whereas)f Fs(R)q Fv(\()p Fs(\021)2697 1170 y Fo(E)2694 1225 y Fp(\006)2758 1203 y Fv(\))g(and)g Fs(T)13 b Fv(\()p Fs(\021)3149 1170 y Fo(E)3146 1225 y Fp(\006)3209 1203 y Fv(\))31 b(ha)m(v)m(e)h(p)s(oles)24 1315 y(at)26 b Fs(E)31 b Fv(=)25 b(+)p Fs(E)462 1329 y Fo(n)508 1315 y Fv(.)39 b(Ob)m(viously)-8 b(,)26 b(the)f(corresp)s(onding)f (re\015ection)h(and)h(transition)e(co)s(e\016cien)m(ts)i Fr(j)p Fs(R)q Fr(j)3292 1282 y Ft(2)3357 1315 y Fv(and)f Fr(j)p Fs(T)13 b Fr(j)3645 1282 y Ft(2)24 1428 y Fv(are)30 b(time-rev)m(ersal)h(in)m(v)-5 b(arian)m(t.)165 1541 y(On)29 b(the)i(other)f(hand)g(the)g(eigenstates)i Fg(f)1585 1508 y Fp(\006)1585 1564 y Fo(n)1674 1541 y Fv(b)s(eha)m(v)m(e)f(as)g (follo)m(ws:)1151 1745 y Fg(f)1181 1707 y Ft(+)1181 1767 y Fo(n)1240 1745 y Fv(\()p Fs(x)25 b Fr(!)g(\0061)p Fv(\))41 b Fr(\030)f Fv(\()p Fr(\006)1923 1664 y Fq(p)p 2014 1664 84 4 v 81 x Fs(i\015)5 b(x)p Fv(\))2184 1707 y Fo(n)2247 1745 y Fs(e)2289 1707 y Fp(\000)p Fo(i)2378 1677 y Fh(\015)p 2378 1692 36 3 v 2381 1733 a Fk(2)2424 1707 y Fo(x)2464 1684 y Fk(2)2532 1745 y Fs(;)941 b Fv(\(6.6\))24 1937 y(and)1143 2050 y Fg(f)1173 2013 y Fp(\000)1173 2073 y Fo(n)1232 2050 y Fv(\()p Fs(x)25 b Fr(!)h(\0061)p Fv(\))40 b Fr(\030)g Fv(\()p Fr(\006)1915 1970 y Fq(p)p 2006 1970 155 4 v 80 x Fr(\000)p Fs(i\015)5 b(x)p Fv(\))2247 2013 y Fo(n)2310 2050 y Fs(e)2352 2013 y Fo(i)2386 1982 y Fh(\015)p 2386 1998 36 3 v 2389 2039 a Fk(2)2432 2013 y Fo(x)2472 1989 y Fk(2)2540 2050 y Fs(:)933 b Fv(\(6.7\))24 2211 y(Note,)40 b(that)e Fg(f)511 2178 y Fp(\000)511 2234 y Fo(n)607 2211 y Fv(are)g(purely)e(outgoing)h(states,)k(whereas)c Fg(f)2108 2178 y Ft(+)2108 2234 y Fo(n)2204 2211 y Fv(are)h(purely)d (ingoing)i(states.)63 b(Moreo)m(v)m(er,)24 2324 y(resonan)m(t)31 b(states)g(ha)m(v)m(e)h(Breit-Wigner)e(energy)h(distribution.)37 b(Indeed,)947 2556 y Fr(h)15 b Fs(\037)1054 2519 y Fo(E)1054 2579 y Fp(\000)1114 2556 y Fr(j)p Fg(f)1169 2519 y Ft(+)1169 2579 y Fo(n)1243 2556 y Fr(i)41 b(\030)f Fv(\000\()p Fr(\000)p Fs(\027)6 b Fv(\))1709 2432 y Fq(Z)1800 2459 y Fp(1)1760 2639 y(\0001)1904 2556 y Fs(D)1979 2570 y Fo(\027)2023 2556 y Fv(\()2058 2476 y Fq(p)p 2149 2476 129 4 v 80 x Fv(2)p Fs(\015)f(i)q(x)p Fv(\))15 b Fg(f)2410 2519 y Ft(+)2410 2579 y Fo(n)2469 2556 y Fv(\()p Fs(x)p Fv(\))g Fs(dx)32 b(:)736 b Fv(\(6.8\))24 2802 y(No)m(w,)32 b Fs(D)332 2816 y Fo(\027)406 2802 y Fv(is)e(an)h(en)m(tire)g(function) f(of)h Fs(\027)37 b Fv(and)30 b(\000\()p Fr(\000)p Fs(\027)6 b Fv(\))31 b(has)g(p)s(oles)f(at)h Fs(\027)h Fv(=)26 b Fs(k)k Fr(2)c Fn(N)7 b Fv(.)48 b(In)30 b(the)i(domain)d(where)24 2915 y Fs(n)19 b Fv(+)h(1)26 b Fs(>)f Fv(Re)15 b Fs(\027)31 b Fr(\025)25 b Fv(1)31 b(one)g(has)995 3166 y(\000\()p Fr(\000)p Fs(\027)6 b Fv(\))26 b(=)f(analytical)k(part)35 b(+)2135 3053 y Fo(n)2091 3080 y Fq(X)2092 3278 y Fo(k)r Ft(=0)2333 3105 y Fv(\()p Fr(\000)p Fv(1\))2519 3072 y Fo(k)p 2247 3145 401 4 v 2247 3229 a Fs(k)s Fv(!\()p Fs(k)24 b Fr(\000)c Fs(\027)6 b Fv(\))2605 3202 y Fo(k)2688 3166 y Fs(:)785 b Fv(\(6.9\))24 3437 y(Hence,)462 3694 y Fr(h)15 b Fs(\037)569 3656 y Fo(E)569 3716 y Fp(\000)629 3694 y Fr(j)p Fg(f)684 3656 y Ft(+)684 3716 y Fo(n)758 3694 y Fr(i)84 b(\030)f Fv(analytical)29 b(function)g(of)38 b Fs(E)j Fv(+)2172 3580 y Fo(n)2128 3607 y Fq(X)2129 3805 y Fo(k)r Ft(=0)2486 3632 y Fv(\()p Fr(\000)p Fv(1\))2672 3599 y Fo(k)p 2284 3673 634 4 v 2284 3788 a Fs(k)s Fv(!)2374 3687 y Fq(\020)2429 3788 y Fs(k)23 b Fv(+)d Fs(i)2631 3753 y Fo(E)p 2631 3768 56 4 v 2639 3820 a(\015)2717 3788 y Fv(+)2818 3753 y Ft(1)p 2818 3768 36 4 v 2818 3820 a(2)2863 3687 y Fq(\021)2943 3694 y Fr(h)15 b Fg(f)3023 3656 y Fp(\000)3023 3723 y Fo(k)3082 3694 y Fr(j)p Fg(f)3137 3656 y Ft(+)3137 3716 y Fo(n)3211 3694 y Fr(i)877 3981 y(\030)83 b Fv(analytical)29 b(function)g(of)38 b Fs(E)j Fv(+)2245 3920 y Fs(\015)p 2122 3960 298 4 v 2122 4044 a(E)26 b Fr(\000)20 b Fs(E)2373 4058 y Fo(n)2460 3981 y Fs(;)968 b Fv(\(6.10\))24 4208 y(whic)m(h)29 b(is)g(consisten)m(t)i (with)e(the)i(Breit-Wigner)f(form)m(ula.)24 4493 y Fu(A)134 b(App)t(endix)24 4696 y Fv(The)29 b(in)m(tegral)i(form)m(ula)e (9.241\(2\))34 b(in)29 b([18)q(])1037 4988 y Fs(D)1112 5003 y Fo(\025)1158 4988 y Fv(\()p Fs(y)s Fv(\))c(=)1438 4926 y Fs(e)1480 4891 y Fp(\000)1545 4860 y Fh(y)1579 4839 y Fk(2)p 1546 4875 68 3 v 1564 4917 a(4)p 1407 4967 252 4 v 1407 5050 a Fv(\000\()p Fr(\000)p Fs(\025)p Fv(\))1699 4864 y Fq(Z)1790 4890 y Fp(1)1749 5070 y(\0001)1894 4988 y Fs(\030)1938 4950 y Fp(\000)p Fo(\025)p Fp(\000)p Ft(1)1934 5011 y(+)2144 4988 y Fs(e)2186 4950 y Fp(\000)p Fo(y)r(\030)s Fp(\000)p Fo(\030)2401 4927 y Fk(2)2435 4950 y Fo(=)p Ft(2)2525 4988 y Fs(d\030)34 b(;)804 b Fv(\(A.1\))1809 5281 y(12)p eop %%Page: 13 13 13 12 bop 24 44 a Fv(con)m(tains)31 b(t)m(w)m(o)i(ob)5 b(jects:)44 b(\000\()p Fr(\000)p Fs(\025)p Fv(\))32 b(and)f(a)g (distribution)d Fs(\030)1981 11 y Fp(\000)p Fo(\025)p Fp(\000)p Ft(1)2203 44 y Fv(whic)m(h)i(are)i(singular)e(for)h Fs(\025)c Fv(=)g(0)p Fs(;)15 b Fv(1)p Fs(;)g Fv(2)p Fs(;)g(:)g(:)g(:)k (:)24 157 y Fv(Ho)m(w)m(ev)m(er,)32 b(it)e(is)g(easy)h(to)g(see)g([14)q (])f(that)1435 362 y Fs(\030)1479 323 y Fp(\000)p Fo(\025)p Fp(\000)p Ft(1)1475 385 y(+)p 1426 407 252 4 v 1426 490 a Fv(\000\()p Fr(\000)p Fs(\025)p Fv(\))1688 268 y Fq(\014)1688 323 y(\014)1688 377 y(\014)1688 432 y(\014)1688 487 y(\014)1718 545 y Fo(p)p Ft(=)p Fo(n)1880 427 y Fv(=)25 b Fs(\016)2019 390 y Ft(\()p Fo(n)p Ft(\))2122 427 y Fv(\()p Fs(\030)t Fv(\))31 b Fs(;)1183 b Fv(\(A.2\))24 715 y(whic)m(h)29 b(sho)m(ws)h(that)h(\(A.1\))h(de\014nes)d(an)h(en)m(tire)h(function)e (of)h Fs(\025)c Fr(2)e Fn(C)18 b Fv(.)47 b(The)30 b(same)g(is)g(true)g (for)1065 1007 y Fs(D)1140 1022 y Fo(\025)1185 1007 y Fv(\()p Fs(y)s Fv(\))c(=)1466 946 y Fs(e)1508 910 y Fp(\000)1573 879 y Fh(y)1607 858 y Fk(2)p 1573 895 68 3 v 1592 936 a(4)p 1435 986 252 4 v 1435 1070 a Fv(\000\()p Fr(\000)p Fs(\025)p Fv(\))1726 884 y Fq(Z)1817 910 y Fp(1)1777 1090 y(\0001)1922 1007 y Fs(\030)1966 969 y Fp(\000)p Fo(\025)p Fp(\000)p Ft(1)1962 1031 y Fp(\000)2171 1007 y Fs(e)2213 970 y Fo(y)r(\030)s Fp(\000)p Fo(\030)2373 946 y Fk(2)2407 970 y Fo(=)p Ft(2)2497 1007 y Fs(d\030)35 b(;)831 b Fv(\(A.3\))24 1248 y(due)29 b(to)1315 1350 y Fs(\030)1359 1312 y Fp(\000)p Fo(\025)p Fp(\000)p Ft(1)1355 1373 y Fp(\000)p 1307 1395 V 1307 1478 a Fv(\000\()p Fr(\000)p Fs(\025)p Fv(\))1568 1257 y Fq(\014)1568 1311 y(\014)1568 1366 y(\014)1568 1420 y(\014)1568 1475 y(\014)1598 1533 y Fo(\025)p Ft(=)p Fo(n)1766 1416 y Fv(=)c(\()p Fr(\000)p Fv(1\))2048 1378 y Fo(n)2096 1416 y Fs(\016)2139 1378 y Ft(\()p Fo(n)p Ft(\))2242 1416 y Fv(\()p Fs(\030)t Fv(\))31 b Fs(:)1063 b Fv(\(A.4\))24 1658 y(The)29 b(second)i(in)m (tegral)f(represen)m(tation)g(giv)m(en)h(b)m(y)f(9.241\(1\))k(in)29 b([18)q(])754 1896 y Fs(D)829 1911 y Fo(\025)875 1896 y Fv(\()p Fs(y)s Fv(\))d(=)1167 1834 y(1)p 1125 1875 131 4 v 1125 1893 a Fr(p)p 1200 1893 56 4 v 1200 1958 a Fs(\031)1281 1896 y Fv(2)1326 1858 y Fo(\025)p Ft(+)1432 1831 y Fk(1)p 1432 1843 31 3 v 1432 1884 a(2)1477 1896 y Fv(\()p Fr(\000)p Fs(i)p Fv(\))1649 1858 y Fo(\025)1695 1896 y Fs(e)1747 1827 y Fh(y)1781 1807 y Fk(2)p 1747 1843 68 3 v 1766 1884 a(4)1859 1772 y Fq(Z)1950 1798 y Fp(1)1910 1978 y(\0001)2039 1896 y Fv(\()p Fs(\030)f Fv(+)20 b Fs(i)p Fv(0\))2341 1858 y Fo(\025)2402 1896 y Fs(e)2444 1858 y Fp(\000)p Ft(2)p Fo(\030)2568 1835 y Fk(2)2603 1858 y Ft(+2)p Fo(iy)r(\030)2807 1896 y Fs(d\030)35 b(;)521 b Fv(\(A.5\))24 2153 y(where)34 b(\()p Fs(\030)28 b Fv(+)23 b Fs(i)p Fv(0\))599 2120 y Fo(\025)678 2153 y Fv(=)32 b Fs(\030)825 2120 y Fo(\025)821 2175 y Ft(+)904 2153 y Fv(+)22 b Fs(e)1039 2120 y Fo(i\031)r(\025)1152 2153 y Fs(\030)1196 2120 y Fo(\025)1192 2175 y Fp(\000)1251 2153 y Fv(,)36 b(seems)f(to)h(ha)m(v)m(e)g(p)s(oles)e(at)i Fs(\025)d Fv(=)f Fr(\000)p Fv(1)p Fs(;)15 b Fr(\000)p Fv(2)p Fs(;)g(:)g(:)g(:)j(:)35 b Fv(Ho)m(w)m(ev)m(er,)j(the)d(limit)24 2266 y(lim)150 2281 y Fo(\025)p Fp(!\000)p Fo(n)363 2266 y Fv(\()p Fs(\030)25 b Fv(+)20 b Fs(i)p Fv(0\))665 2233 y Fo(\025)742 2266 y Fv(is)29 b(w)m(ell)g(de\014ned)h([14)q(])1037 2514 y(\()p Fs(\030)25 b Fv(+)20 b Fs(i)p Fv(0\))1339 2477 y Fp(\000)p Fo(n)1467 2514 y Fv(=)25 b Fs(\030)1607 2477 y Fp(\000)p Fo(n)1729 2514 y Fr(\000)1830 2453 y Fs(i\031)s Fv(\()p Fr(\000)p Fv(1\))2102 2420 y Fo(n)p Fp(\000)p Ft(1)p 1830 2493 411 4 v 1881 2577 a Fv(\()p Fs(n)c Fr(\000)e Fv(1\)!)2265 2514 y Fs(\016)2308 2477 y Ft(\()p Fo(n)p Fp(\000)p Ft(1\))2501 2514 y Fv(\()p Fs(\030)t Fv(\))31 b Fs(:)804 b Fv(\(A.6\))24 2756 y(Th)m(us,)29 b(form)m(ula)h(\(A.5\))i(also)e(de\014nes)f(an)i(en)m(tire)f(function)f (of)i Fs(\025)p Fv(.)24 3041 y Fu(Ac)l(kno)l(wledgmen)l(ts)24 3244 y Fv(I)d(w)m(ould)f(lik)m(e)h(to)i(thank)e(Andrzej)g(Kossak)m(o)m (wski)h(for)g(man)m(y)f(in)m(teresting)g(and)g(stim)m(ulating)f (discussions.)24 3528 y Fu(References)69 3731 y Fv([1])46 b(D.)66 b(Chru)-5 b(\023)-41 b(sci)s(\023)-48 b(nski,)70 b(Quan)m(tum)64 b(Mec)m(hanics)h(of)g(Damp)s(ed)f(Systems,)73 b(LANL)65 b(e-prin)m(t)f(math-)210 3844 y(ph/0301024)33 b(\(to)f(app)s(ear)e(in)f(J.)h(Math.)h(Ph)m(ys.\))69 4028 y([2])46 b(A.)38 b(Bohm)f(and)f(M.)i(Gadella,)g Ff(Dir)-5 b(ac)39 b(Kets,)h(Gamov)g(V)-7 b(e)i(ctors)39 b(and)h(Gel'fand)g(T)-7 b(riplets)p Fv(,)40 b(Lecture)210 4141 y(Notes)32 b(in)d(Ph)m(ysics)h Fw(348)p Fv(,)h(Springer,)d (Berlin,)h(1989)69 4325 y([3])46 b(A.)29 b(Bohm,)h(H.-D.)f(Do)s(ebner,) g(P)-8 b(.)29 b(Kielano)m(wski,)f Ff(Irr)-5 b(eversibility)31 b(and)h(Causality,)h(Semigr)-5 b(oups)32 b(and)210 4438 y(R)n(igge)-5 b(d)33 b(Hilb)-5 b(ert)33 b(Sp)-5 b(ac)g(es)p Fv(,)32 b(Lecture)f(Notes)g(in)e(Ph)m(ysics)h Fw(504)p Fv(,)h(Springer,)e(Berlin,)g(1998.)69 4622 y([4])46 b(S.)41 b(Alb)s(ev)m(erio,)h(L.S.)f(F)-8 b(erreira)40 b(and)g(L.)h(Streit,)i (eds.)d Ff(R)-5 b(esonanc)g(es)44 b({)f(Mo)-5 b(dels)43 b(and)g(Phenomena)p Fv(,)210 4735 y(Lecture)31 b(Notes)h(in)d(Ph)m (ysics)g Fw(211)p Fv(,)j(Springer,)c(Berlin,)h(1984)69 4919 y([5])46 b(E.)35 b(Brandas)g(and)f(N.)h(Elander,)f(eds.)h Ff(R)-5 b(esonanc)g(es)p Fv(,)38 b(Lecture)d(Notes)h(in)d(Ph)m(ysics)h Fw(325)p Fv(,)j(Springer,)210 5032 y(Berlin,)29 b(1989)1809 5281 y(13)p eop %%Page: 14 14 14 13 bop 69 44 a Fv([6])46 b(G.)31 b(P)m(arra)m(vicini,)f(V.)g(Gorini) f(and)h(E.C.G.)h(Sudarshan,)d(J.)i(Math.)i(Ph)m(ys.)e Fw(21)h Fv(\(1980\))i(2208.)69 232 y([7])46 b(E.C.)31 b(Kem)m(ble,)f(Ph)m(ys.)g(Rev.)h Fw(48)g Fv(\(1935\))i(549)69 419 y([8])46 b(K.W.)31 b(F)-8 b(ord,)31 b(D.L.)g(Hill,)e(M.)i(W)-8 b(ak)j(ano)32 b(and)e(J.A.)g(Wheeler,)h(Ann.)f(Ph)m(ys.)g Fw(7)g Fv(\(1959\))j(239)69 607 y([9])46 b(W.A.)32 b(F)-8 b(riedman)29 b(and)h(C.J.)g(Go)s(eb)s(el,)g(Ann.)g(Ph)m(ys.)g Fw(104)h Fv(\(1977\))i(145)24 795 y([10])46 b(G.)31 b(Barton,)h(Ann.)d (Ph)m(ys.)i Fw(166)g Fv(\(1986\))i(322)24 982 y([11])46 b(N.L.)31 b(Balazs)g(and)f(A.)h(V)-8 b(oros,)31 b(Ann.)f(Ph)m(ys.)g Fw(199)i Fv(\(1990\))g(123)24 1170 y([12])46 b(M.)37 b(Castagnino,)g(R.)f(Diener,)h(L.)f(Lara)g(and)f(G.)i(Puccini,)e(In)m (t.)i(Jour.)e(Theor.)g(Ph)m(ys.)h Fw(36)h Fv(\(1997\))210 1283 y(2349)24 1470 y([13])46 b(T.)31 b(Shim)m(b)s(ori)c(and)j(T.)g (Koba)m(y)m(ashi,)h(Nuo)m(v)m(o)g(Cimen)m(to)f(B)h Fw(115)g Fv(\(2000\))i(325)24 1658 y([14])46 b(I.M.)26 b(Gel'fand)e(and)h(G.E.)g (Shilo)m(v,)g Ff(Gener)-5 b(alize)g(d)29 b(functions)p Fv(,)e(V)-8 b(ol.)25 b(I,)g(Academic)g(Press,)h(New)f(Y)-8 b(ork,)210 1771 y(1966)24 1959 y([15])46 b(R.P)-8 b(.)38 b(Kan)m(w)m(al,)g Ff(Gener)-5 b(alize)g(d)40 b(F)-7 b(unctions:)54 b(The)-5 b(ory)39 b(and)g(T)-7 b(e)i(chniques)p Fv(,)39 b(Mathematics)e(in)e(Science)210 2072 y(and)30 b(Engineering)f Fw(177)p Fv(,)i(Academic)g(Press,)f(New)h(Y)-8 b(ork,)31 b(1983)24 2259 y([16])46 b(A.)31 b(Kossak)m(o)m(wski,)g(priv)-5 b(ate)30 b(comm)m(unication)24 2447 y([17])46 b(L.D.)32 b(Landau)d(and)h(E.M.)h(Lifshitz,)e Ff(Quantum)k(Me)-5 b(chanics)p Fv(,)31 b(P)m(ergamon,)g(London,)f(1958)24 2634 y([18])46 b(I.)35 b(Gradsh)m(teyn)g(and)f(I.)g(Ryzhik,)h Ff(T)-7 b(able)37 b(of)g(Inte)-5 b(gr)g(als,)39 b(Series)d(and)i(Pr)-5 b(o)g(ducts)p Fv(,)37 b(Academic)e(Press,)210 2747 y(1965)24 2935 y([19])46 b(P)-8 b(.M.)31 b(Morse)g(and)e(H.)i(F)-8 b(esh)m(bac)m(h,)31 b Ff(Metho)-5 b(ds)34 b(of)e(The)-5 b(or)g(etic)g(al)35 b(Physics)p Fv(,)30 b(McGra)m(w-Hill,)g(New)g(Y)-8 b(ork,)210 3048 y(1953)24 3236 y([20])46 b(M.)23 b(Abramo)m(witz)f(and) f(I.)h(Stegun,)h Ff(Handb)-5 b(o)g(ok)27 b(of)e(Mathematic)-5 b(al)27 b(F)-7 b(unctions)p Fv(,)24 b(Do)m(v)m(er)g(Publications,)210 3348 y(New)31 b(Y)-8 b(ork,)31 b(1972)24 3536 y([21])46 b(P)-8 b(.L.)31 b(Duren,)f Ff(The)-5 b(ory)35 b(of)d Fr(H)1199 3503 y Fo(p)1271 3536 y Ff(Sp)-5 b(ac)g(es)p Fv(,)32 b(Academic)f(Press,)f(New)h(Y)-8 b(ork,)31 b(1970)24 3724 y([22])46 b(I.M.)31 b(Gel'fand)f(and)f(N.Y.)i(Vilenkin,)c Ff(Gener)-5 b(alize)g(d)35 b(F)-7 b(unctions)p Fv(,)31 b(V)-8 b(ol.)30 b(IV,)h(Academic)f(Press,)g(New)210 3837 y(Y)-8 b(ork,)32 b(1964.)24 4024 y([23])46 b(K.)22 b(Maurin,)g Ff(Gener)-5 b(al)26 b(Eigenfunction)e(Exp)-5 b(ansion)26 b(and)f(Unitary)g(R)-5 b(epr)g(esentations)28 b(of)d(T)-7 b(op)i(olo)g(gic)g(al)210 4137 y(Gr)g(oups)p Fv(,)33 b(PWN,)e(W)-8 b(arsza)m(w)m(a,)33 b(1968.)1809 5281 y(14)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0309050237747--