Content-Type: multipart/mixed; boundary="-------------0612140953933" This is a multi-part message in MIME format. ---------------0612140953933 Content-Type: text/plain; name="06-362.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="06-362.comments" werner.amrein@physics.unige.ch philippe.jacquet@physics.unige.ch ---------------0612140953933 Content-Type: text/plain; name="06-362.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="06-362.keywords" Scattering theory, Time delay ---------------0612140953933 Content-Type: application/postscript; name="Paper-Definitive.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="Paper-Definitive.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %%Title: Paper-Definitive.dvi %%Pages: 48 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX12 CMR12 CMSY8 CMTI12 CMR10 CMMI10 CMSY10 CMMI8 %%+ CMSY7 CMTT10 CMBX10 CMMI12 CMR8 CMMI6 MSBM10 CMR17 CMEX10 CMR6 MSBM7 %%+ CMTI10 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips Paper-Definitive.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2006.10.25:1009 %%BeginProcSet: texc.pro %! 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 82 /R put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueID 5032014 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 2 /bracketleftbig put dup 3 /bracketrightbig put dup 8 /braceleftbig put dup 9 /bracerightbig put dup 12 /vextendsingle put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 34 /bracketleftBigg put dup 35 /bracketrightBigg put dup 48 /parenlefttp put dup 49 /parenrighttp put dup 64 /parenleftbt put dup 65 /parenrightbt put dup 80 /summationtext put dup 82 /integraltext put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 99 /hatwider put dup 100 /hatwidest put dup 112 /radicalbig put readonly def 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A 27D1663E0B62F461F6E40A5D6676D1D12B51E641C1D4E8E2771864FC104F8CBF 5B78EC1D88228725F1C453A678F58A7E1B7BD7CA700717D288EB8DA1F57C4F09 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%!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F00F963068B8B731A88D7740B0DDAED1B3F82 7DB9DFB4372D3935C286E39EE7AC9FB6A9B5CE4D2FAE1BC0E55AE02BFC464378 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-4 -235 731 800}readonly def /UniqueID 5000832 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F00F963068B8232429ED8B7CF6A3D879A2D19 38DD5C4467F9DD8C5D1A2000B3A6BF2F25629BAEC199AE8BD4BA6ED9BBF7DABF 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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-36 -251 1103 750}readonly def /UniqueID 5000829 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 525003F3DBE5BF07B2E83E66B7F97DDD7CE0EEB75A78BD9227BF359D002B6ADB 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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Fr(\022)2593 4913 y Fm(')p Fy(\()p Fm(x)g Fy(+)g Fm(x)2925 4928 y Fk(0)2965 4913 y Fy(\))p Fl(j)3031 4872 y Fk(2)3087 4913 y Fm(dx)519 b Fy(\(17\))0 5186 y(and)33 b(for)f Fm(t)c(<)f Fy(0:)643 5324 y Fe(Z)743 5350 y Fx(1)698 5549 y Fr(x)738 5558 y Fd(0)834 5459 y Fl(j)p Fm(')926 5474 y Fr(t)955 5459 y Fy(\()p Fm(x)p Fy(\))p Fl(j)1114 5418 y Fk(2)1170 5459 y Fm(dx)h Fl(\024)g Fm(C)1479 5474 y Fr(\022)1518 5459 y Fy(\(1)22 b(+)g Fl(j)p Fm(t)p Fl(j)p Fy(\))1854 5418 y Fx(\000)p Fr(\022)1964 5324 y Fe(Z)2063 5350 y Fx(1)2019 5549 y(\0001)2165 5459 y Fl(j)p Fy(\(1)g(+)g Fl(j)p Fm(x)p Fl(j)p Fy(\))2549 5418 y Fr(\022)2588 5459 y Fm(')p Fy(\()p Fm(x)g Fy(+)g Fm(x)2920 5474 y Fk(0)2960 5459 y Fy(\))p Fl(j)3026 5418 y Fk(2)3082 5459 y Fm(dx)27 b(:)470 b Fy(\(18\))p Black 1870 5774 a(8)p Black eop end %%Page: 9 9 TeXDict begin 9 8 bop Black Black 0 83 a Fy(\(b\))32 b(Let)h Fm(')f Fy(b)s(e)g(a)g(w)m(a)m(v)m(e)i(pac)m(k)m(et)g(with)f (negativ)m(e)g(momen)m(tum)h(\(i.e.,)49 b(^)-65 b Fm(')p Fy(\()p Fm(p)p Fy(\))27 b(=)h(0)k(for)g Fm(p)27 b Fl(\025)h Fy(0\),)33 b Fm(x)3463 98 y Fk(0)3530 83 y Fl(2)28 b Fh(R)k Fy(and)0 257 y Fm(\022)f(>)c Fy(0.)44 b(Then)33 b(there)h(exists)g(a)e(constan)m(t)i Fm(C)1617 272 y Fr(\022)1688 257 y Fy(so)f(that)f(for)g Fm(t)c(>)g Fy(0:)698 396 y Fe(Z)798 422 y Fx(1)753 621 y Fr(x)793 630 y Fd(0)889 531 y Fl(j)p Fm(')981 546 y Fr(t)1010 531 y Fy(\()p Fm(x)p Fy(\))p Fl(j)1169 490 y Fk(2)1225 531 y Fm(dx)g Fl(\024)g Fm(C)1534 546 y Fr(\022)1573 531 y Fy(\(1)22 b(+)g Fm(t)p Fy(\))1853 490 y Fx(\000)p Fr(\022)1964 396 y Fe(Z)2063 422 y Fx(1)2019 621 y(\0001)2165 531 y Fl(j)p Fy(\(1)g(+)g Fl(j)p Fm(x)p Fl(j)p Fy(\))2549 490 y Fr(\022)2587 531 y Fm(')p Fy(\()p Fm(x)h Fy(+)f Fm(x)2920 546 y Fk(0)2960 531 y Fy(\))p Fl(j)3026 490 y Fk(2)3081 531 y Fm(dx)525 b Fy(\(19\))0 805 y(and)33 b(for)f Fm(t)c(<)f Fy(0:)638 944 y Fe(Z)737 970 y Fr(x)777 979 y Fd(0)693 1169 y Fx(\0001)839 1079 y Fl(j)p Fm(')931 1094 y Fr(t)960 1079 y Fy(\()p Fm(x)p Fy(\))p Fl(j)1119 1038 y Fk(2)1175 1079 y Fm(dx)h Fl(\024)g Fm(C)1484 1094 y Fr(\022)1523 1079 y Fy(\(1)22 b(+)g Fl(j)p Fm(t)p Fl(j)p Fy(\))1859 1038 y Fx(\000)p Fr(\022)1969 944 y Fe(Z)2069 970 y Fx(1)2024 1169 y(\0001)2171 1079 y Fl(j)p Fy(\(1)f(+)h Fl(j)p Fm(x)p Fl(j)p Fy(\))2554 1038 y Fr(\022)2593 1079 y Fm(')p Fy(\()p Fm(x)g Fy(+)g Fm(x)2925 1094 y Fk(0)2965 1079 y Fy(\))p Fl(j)3031 1038 y Fk(2)3087 1079 y Fm(dx)28 b(:)464 b Fy(\(20\))0 1353 y(\(c\))32 b(Let)h Fm(f)43 b Fy(b)s(e)32 b(a)g(function)h(satisfying)g Fl(j)p Fm(f)11 b Fy(\()p Fm(x)p Fy(\))p Fl(j)27 b(\024)i Fm(C)7 b Fy(\(1)21 b(+)g Fl(j)p Fm(x)p Fl(j)p Fy(\))2256 1317 y Fx(\000)p Fr(\026)2389 1353 y Fy(for)32 b(all)g Fm(x)c Fl(2)h Fh(R)p Fy(,)j(some)h(constan)m(t)g Fm(C)39 b Fy(and)0 1528 y(some)34 b Fm(\026)27 b(>)h Fy(0.)43 b(Let)33 b Fm(')g Fy(b)s(e)g(a)f(w)m(a)m(v)m(e)j(pac)m(k)m(et)f(with)f (momen)m(tum)h(in)f Fh(R)23 b Fl(n)f Fy(\()p Fl(\000)p Fm(p)2764 1543 y Fk(0)2803 1528 y Fm(;)17 b(p)2896 1543 y Fk(0)2936 1528 y Fy(\))32 b(for)g(some)i Fm(p)3449 1543 y Fk(0)3516 1528 y Fm(>)28 b Fy(0,)k(and)0 1702 y(let)h Fm(\022)e(>)c Fy(0.)44 b(Then)33 b(there)h(exists)g(a)e (constan)m(t)i Fm(C)1758 1717 y Fr(\022)1829 1702 y Fy(so)f(that)f(for) g(all)h Fm(t)28 b Fl(2)g Fh(R)p Fy(:)173 1840 y Fe(Z)272 1867 y Fx(1)228 2066 y(\0001)374 1976 y Fl(j)p Fm(f)11 b Fy(\()p Fm(x)p Fy(\))p Fm(')656 1991 y Fr(t)686 1976 y Fy(\()p Fm(x)p Fy(\))p Fl(j)845 1935 y Fk(2)901 1976 y Fm(dx)27 b Fl(\024)i Fm(C)1210 1991 y Fr(\022)1265 1835 y Fe(\024)1490 1909 y Fy(1)p 1328 1953 375 4 v 1328 2044 a(\(1)21 b(+)h Fl(j)p Fm(t)p Fl(j)p Fy(\))1663 2015 y Fr(\022)1734 1976 y Fy(+)2095 1909 y(1)p 1842 1953 555 4 v 1842 2044 a(\(1)g(+)g(2)p Fm(p)2147 2059 y Fk(0)2186 2044 y Fl(j)p Fm(t)p Fl(j)p Fy(\))2315 2015 y Fk(2)p Fr(\026)2406 1835 y Fe(\025)2476 1840 y(Z)2575 1867 y Fx(1)2531 2066 y(\0001)2677 1976 y Fl(j)p Fy(\(1)g(+)g Fl(j)p Fm(x)p Fl(j)p Fy(\))3061 1935 y Fr(\022)3099 1976 y Fm(')p Fy(\()p Fm(x)p Fy(\))p Fl(j)3322 1935 y Fk(2)3378 1976 y Fm(dx)28 b(:)173 b Fy(\(21\))125 2250 y(Of)29 b(course)i(the)f(ab)s(o)m(v)m(e)g(estimates)h(are)f(useful)h(only)f(if) f(the)i(in)m(tegrals)f(on)g(the)g(r.h.s.)g(are)g(\014nite.)43 b(This)0 2424 y(requiremen)m(t)32 b(essen)m(tially)g(amoun)m(ts)e(to)f (a)g(di\013eren)m(tiabilit)m(y)j(prop)s(ert)m(y)e(of)f(the)h(F)-8 b(ourier)29 b(transform)h(of)f Fm(')0 2599 y Fy(\()16 b(^)-65 b Fm(')32 b Fy(should)i(b)s(e)f Fm(\022)i Fy(times)f (di\013eren)m(tiable)g(in)f(some)g(sense\).)125 2968 y Fn(B.)104 b(Time)35 b(deca)m(y)h(in)f(a)f(non-constan)m(t)i(p)s(oten) m(tial)125 3261 y Fy(Results)43 b(on)f(time)h(deca)m(y)h(of)e(w)m(a)m (v)m(e)i(pac)m(k)m(ets)h(in)d(a)h(non-constan)m(t)f(p)s(oten)m(tial)h (are)g(not)f(so)g(easy)i(to)0 3435 y(obtain.)79 b(The)45 b(time)g(ev)m(olution)h(is)f(no)m(w)g(giv)m(en)g(b)m(y)g(the)g(unitary) g(op)s(erators)f(exp)q(\()p Fl(\000)p Fm(iH)8 b(t)p Fy(\),)48 b(and)d(it)f(is)0 3609 y(useful)c(to)f(relate)g(them)g(to)g(the)g (Green's)h(op)s(erator)e(\()p Fm(H)c Fl(\000)27 b Fm(z)t Fy(\))2347 3573 y Fx(\000)p Fk(1)2442 3609 y Fy(,)41 b(with)e Fm(z)k Fl(2)c Fh(C)27 b Fl(n)f Fh(R)p Fy(.)62 b(F)-8 b(or)38 b Fm(\017)h(>)g Fy(0)f(and)0 3784 y Fm(E)c Fl(2)28 b Fh(R)k Fy(w)m(e)i(set)782 3958 y Fm(\016)825 3973 y Fk(\()p Fr(\017)p Fk(\))912 3958 y Fy(\()p Fm(H)c Fl(\000)23 b Fm(E)6 b Fy(\))27 b(=)1464 3891 y(1)p 1418 3935 141 4 v 1418 4026 a(2)p Fm(\031)t(i)1569 3958 y Fy([\()p Fm(H)i Fl(\000)23 b Fm(E)28 b Fl(\000)23 b Fm(i\017)p Fy(\))2154 3917 y Fx(\000)p Fk(1)2271 3958 y Fl(\000)g Fy(\()p Fm(H)29 b Fl(\000)23 b Fm(E)28 b Fy(+)22 b Fm(i\017)p Fy(\))2927 3917 y Fx(\000)p Fk(1)3022 3958 y Fy(])28 b Fm(:)608 b Fy(\(22\))0 4186 y(Then)1118 4361 y Fm(\016)1161 4376 y Fk(\()p Fr(\017)p Fk(\))1249 4361 y Fy(\()p Fm(H)30 b Fl(\000)22 b Fm(E)6 b Fy(\))28 b(=)1784 4293 y(1)p 1755 4338 108 4 v 1755 4429 a(2)p Fm(\031)1889 4225 y Fe(Z)1988 4251 y Fx(1)1944 4451 y(\0001)2090 4361 y Fm(e)2135 4320 y Fr(iE)t(t)2245 4361 y Fm(e)2290 4320 y Fx(\000)p Fr(iH)5 b(t)p Fx(\000)p Fr(\017)p Fx(j)p Fr(t)p Fx(j)2626 4361 y Fm(dt)28 b(:)945 b Fy(\(23\))0 4601 y(If)41 b Fm( )46 b Fy(is)c(a)f(\(square-in)m(tegrable\))i(w)m(a)m(v)m(e)g (function,)i(w)m(e)d(set)h Fm( )2301 4616 y Fr(t)2373 4601 y Fy(=)g Fm(e)2537 4565 y Fx(\000)p Fr(iH)5 b(t)2709 4601 y Fm( )45 b Fy(and)d(obtain)f(from)h(\(23\))e(b)m(y)0 4776 y(using)33 b(the)g(Planc)m(herel)i(theorem)e(that,)g(for)f(an)m(y) h(b)s(ounded)g(op)s(erator)f Fm(B)5 b Fy(:)221 4914 y Fe(Z)321 4940 y Fx(1)276 5140 y(\0001)423 5050 y Fm(dt)526 4914 y Fe(Z)625 4940 y Fx(1)580 5140 y(\0001)727 5050 y Fm(dx)32 b(e)910 5008 y Fx(\000)p Fk(2)p Fr(\017)p Fx(j)p Fr(t)p Fx(j)1098 5050 y Fl(j)p Fy(\()p Fm(B)5 b( )1306 5065 y Fr(t)1336 5050 y Fy(\)\()p Fm(x)p Fy(\))p Fl(j)1533 5008 y Fk(2)1600 5050 y Fy(=)27 b(2)p Fm(\031)1828 4914 y Fe(Z)1927 4940 y Fx(1)1883 5140 y(\0001)2029 5050 y Fm(dE)2175 4914 y Fe(Z)2274 4940 y Fx(1)2230 5140 y(\0001)2376 5050 y Fm(dx)33 b Fl(j)p Fy([)p Fm(B)5 b(\016)2692 5065 y Fk(\()p Fr(\017)p 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Fm(\037)1531 3375 y Fr(`)1564 3360 y Fm(e)1609 3324 y Fx(\000)p Fr(iH)1746 3332 y Fi(\024)1786 3324 y Fr(t)1854 3360 y Fy(represen)m(ts)h(the)e(observ)-5 b(able)39 b(of)e(lo)s(calization)g(on)h(the)0 3535 y(left)i(at)g Fm(t)h Fy(=)g(+)p Fl(1)f Fy(in)g(a)g(constan)m(t)i(p)s(oten)m(tial;)i (it)c(do)s(es)h(not)f(dep)s(end)i(on)e Fm(\024)g Fy(and)h(will)g(b)s(e) f(denoted)h(b)m(y)0 3709 y Fm(F)77 3668 y Fk(+)63 3737 y(0)p Fr(;`)151 3709 y Fy(.)63 b(So)39 b Fm(F)460 3668 y Fk(+)446 3737 y(0)p Fr(;`)573 3709 y Fy(is)g(the)h(\(orthogonal\))e (pro)5 b(jection)40 b(on)m(to)f(the)g(subspace)i Fl(H)2791 3668 y Fk(+)2790 3737 y(0)p Fr(;`)2917 3709 y Fy(of)e(w)m(a)m(v)m(e)i (functions)f(that)0 3883 y(are)j(lo)s(calized)h(on)f(the)g(left)h(at)e Fm(t)k Fy(=)g(+)p Fl(1)c Fy(\(in)h(a)g(constan)m(t)h(p)s(oten)m (tial\),)i(and)d(it)g(coincides)i(with)f(the)0 4058 y(pro)5 b(jection)33 b(\005)536 4073 y Fx(\000)628 4058 y Fy(on)m(to)g(the)g (subspace)h Fl(H)1507 4073 y Fx(\000)1599 4058 y 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