ASYMPTOTIC OF THE DENSITY-OF-STATES FOR THE SCHRODINGER OPERATOR WITHPERIODIC ELECTROMAGNETIC POTENTIAL

For the Schrojdinger operator in L-2(R-n), n>1, with C-infinity period ic electromagnetic potential, we give an asymptotic formula of the int egrate density of states of the form N(mu) = a(n) mu(n/2)+ O(mu((n-2+e psilon)/2), For All epsilon>0. When n=2, this estimate enables us to p rove the finiteness of gaps in the spectrum. (C) 1997 American Institu te of Physics.