Asymptotic behavior of the discrete spectrum of the Schrödinger operator in electric and homogeneous magnetic fields

Abstract

The asymptotic behavior of bound states is considered to the left of the boundary of the essential spectrum of the Schrodinger operator in homogeneous magnetic and decreasing electric fields. The electric potential is not considered nonpositive. It is assumed that the integral of the potential along the direction of the magnetic field has a powerlike behavior at infinity. It is shown that the asymptotic behavior of the bound states is powerlike and its leading term is computed.