Sharp Spectral Asymptotics for Operators with Irregular Coefficients. IV. Multidimensional Schroedinger operator with a strong magnetic field. Full-rank case

Abstract

With derive sharp spectral asymptotics (with the remainder estimate $O(μ^{-1}h^{1-d}+μ^{\frac{d} {2}-1}h^{1-\frac{d}{2}})$ for $d$-dimensional Schrödinger operator with a strong magnetic field; here $h$ and $μ$ are Plank and binding constants respectively and magnetic intensity matrix has full rank at each point. In comparison with version 1 of 4.5 year ago this version contains more results (we also study some degenerations), improvements and some minor corrections.