# Abstract

We consider the magnetic Schrödinger operator H
in dimension d with metric, magnetic potential, and electric
potential. All coefficients are supposed to be periodic with respect
to some lattice. The Floquet theory shows that the spectrum of H has
a band structure. Ruling out the possibility for some bands to
degenerate into points is a more subtle problem. The absence of
degenerate bands is equivalent to absolute continuity of the
spectrum. For the periodic operator Schrödinger operator with
electric potential only the absence of degenerate bands was proved by
L. Thomas in 1973. Thomas suggested an original method of analytic
continuation in the complex quasimomentum. In recent years the problem
of absolute continuity of the spectrum of H has been intensively
studied. We propose a survey of the recent results and unsolved
problems in this area.
Heinz Siedentop