 97653 Abderemane MOHAMED
 Asymptotic of the density of states for Schrodinger operator with periodic
electromagnetic potential
(83K, LATeX 2e)
Dec 30, 97

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Abstract. For the Schr\"odinger operator
in $L^2({\bf R}^n),\ n>1,$
with $C^{\infty }$ periodic electromagnetic potential,
we give an asymptotic formula of
the integrate density of states
of the form
$$ N(\mu )=a_n\mu ^{n/2}+
{\bf O}(\mu ^{(n2+\epsilon )/2}),\
\ \forall \ \epsilon >0.$$
When $n=2,$ this estimate enables us to prove the finiteness of gaps
in the spectrum.
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