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

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 $O(μ^{-1}h^{-1}+1)$ 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 $μ^3h\ge 2$ then asymptotics contains correction terms of magnitude $μ^{-1}h^{-1}|\log μ^3 h|$.