On Spectral Theory for Schrödinger Operators with Magnetic Potentials

Abstract

In this survey, we want to analyze the effect of the presence of a magnetic potential on the spectrum of the Schrödinger operator with magnetic field. We consider three connected problems:

• study of the bottom of the spectrum

• study of the bottom of the essential spectrum

• study of the decay of the eigenfunctions.

We think this survey is complementary to other presentations of the subject in [12], [20] and [49].