Sharp Spectral Asymptotics for four-dimensional Schroedinger operator with a strong magnetic field. II

Abstract

I consider 4-dimensional Schrödinger operator with the generic non-degenerating magnetic field and for a generic potential I derive spectral asymptotics with the remainder estimate $O({\mu }^{-1}{h}^{-3})$ and the principal part $\asymp h^{-4}$ where $h\ll 1$ is Planck constant and $\mu \gg 1$ is the intensity of the magnetic field. For general potentials remainder estimate $O({\mu }^{-1}{h}^{-3}+{\mu }^2{h}^{-2})$ is achieved.

57pp