On the Spectrum¶of Two-Dimensional Schrödinger Operators¶with Spherically Symmetric, Radially Periodic¶Magnetic Fields

Abstract:

We investigate the spectrum of the two-dimensional Schrödinger operator , where the magnetic field and the electric potential V are spherically symmetric, i.e., , , and b is p-periodic, similarly for V. By considering two different gauges we get the following results: In case the spectrum contains a semi-axis that consists alternately of intervals of absolutely continuous and dense point spectrum. In case the essential spectrum is purely dense point spectrum and possibly there are spectral gaps.