Sharp Spectral Asymptotics for 2-dimensional Schrödinger operator with a strong but degenerating magnetic field. II

Abstract

I consider the same operator as in part I assuming however that $μ\ge Ch^{-1}$ and $V$ is replaced by $(2l+1)μh F+W$ with $l\in \bZ^+$. Under some non-degeneracy conditions I recover remainder estimates up to $O \bigl(μ^{-{\frac 1 ν}}h^{-1} +1\bigr)$ but now case $μ\ge Ch^{-ν}$ is no more forbidden and the principal part is of magnitude $μh^{-1}$.