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

2006/03/04 by Victor Ivrii, Ivrii, Victor
Mathematics · #35P20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP) #math.AP #math.SP #msc:35P20

paper · pdf · doi:10.48550/arxiv.math/0603118

6 pp

arxiv created 2006/03/04 · arxiv updated 2009/12/01

Abstract

I consider magnetic Schrödinger operator in dimension d=2 assuming that coefficients are smooth and magnetic field is non-degenerating. Then I extend the remainder estimate O(μ^-1h^-1+1) derived in \citeIvr1 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 μ³h≥ 2 then asymptotics contains correction terms of magnitude μ^-1h^-1|log μ³ h|.

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