Abderemane MOHAMED
Asymptotic of the density of states for Schrodinger operator with periodic
electro-magnetic potential
(83K, LATeX 2e)
ABSTRACT. For the Schr\"odinger operator
in $L^2({\bf R}^n),\ n>1,$
with $C^{\infty }$ periodic electro-magnetic potential,
we give an asymptotic formula of
the integrate density of states
of the form
$$ N(\mu )=a_n\mu ^{n/2}+
{\bf O}(\mu ^{(n-2+\epsilon )/2}),\
\ \forall \ \epsilon >0.$$
When $n=2,$ this estimate enables us to prove the finiteness of gaps
in the spectrum.