Discrete spectrum of Schrödinger operators with perturbed uniform magnetic fields (Q1911594)

A nonlinear Schrödinger operator \(H\) with a magnetic field is studied in 3D space. The aim of the paper is to clarify the relation between the scalar and vector potentials for \(H\) to have an infinite or finite discrete spectrum. The main theorem gives sufficient conditions for the cardinal number of the discrete spectrum to be infinite. On the other hand, examples of various potentials are presented, for which the discrete spectrum of \(H\) is finite.