On estimation of the number of eigenvalues of the magnetic Schrödinger operator in a three-dimensional layer

Abstract

In this paper, we study the magnetic Schrödinger operator in a three-dimensional layer. We obtain an estimate for the number of eigenvalues of this operator lying to the left of the essential spectrum threshold. We show that the magnetic Schrödinger operator to the left of the continuous spectrum threshold can have only a finite number of eigenvalues of infinite multiplicity.