Sharp Spectral Asymptotics for 2-dimensional Schrödinger operator with a strong magnetic field. Note about forgotten generic case

Details Sharp Spectral Asymptotics for 2-dimensional Schrödinger operator with a strong magnetic field. Note about forgotten generic case Sharp Spectral Asymptotics for 2-dimensional Schrödinger operator with a strong magnetic field. Note about forgotten generic case

2006-03-04

arxiv.org/abs/math/0603118v1

Mathematics

Analysis of PDEs

6 pp

Scientific paper

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

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