English

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

Analysis of PDEs 2007-05-23 v1 Spectral Theory

Abstract

I consider 4-dimensional Schr\"odinger operator with the generic non-degenerating magnetic field and for a generic potential I derive spectral asymptotics with the remainder estimate O(μ1h3)O(\mu^{-1}h^{-3}) and the principal part h4\asymp h^{-4} where h1h\ll 1 is Planck constant and μ1\mu \gg 1 is the intensity of the magnetic field. For general potentials remainder estimate O(μ1h3+μ2h2)O(\mu^{-1}h^{-3}+\mu^2h^{-2}) is achieved.

Keywords

Cite

@article{arxiv.math/0612252,
  title  = {Sharp Spectral Asymptotics for four-dimensional Schroedinger operator with a strong magnetic field. II},
  author = {Victor Ivrii},
  journal= {arXiv preprint arXiv:math/0612252},
  year   = {2007}
}

Comments

57pp

R2 v1 2026-07-22T17:47:37.147Z