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Sharp Spectral Asymptotics for 2-dimensional Schr\"odinger operator with a strong magnetic field. Note about forgotten generic case

Analysis of PDEs 2007-05-23 v1 Spectral Theory

Abstract

I consider magnetic Schr\"odinger operator in dimension d=2d=2 assuming that coefficients are smooth and magnetic field is non-degenerating. Then I extend the remainder estimate O(μ1h1+1)O(\mu^{-1}h^{-1}+1) derived in \cite{Ivr1} for the case when V/FV/F has no stationary points to the case when it has non-degenerating stationary points. If some of them are saddles and μ3h2\mu^3h\ge 2 then asymptotics contains correction terms of magnitude μ1h1logμ3h\mu^{-1}h^{-1}|\log \mu^3 h|.

Keywords

Cite

@article{arxiv.math/0603118,
  title  = {Sharp Spectral Asymptotics for 2-dimensional Schr\"odinger operator with a strong magnetic field. Note about forgotten generic case},
  author = {Victor Ivrii},
  journal= {arXiv preprint arXiv:math/0603118},
  year   = {2007}
}

Comments

6 pp

R2 v1 2026-07-22T17:32:27.868Z