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

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

2005-10-16

arxiv.org/abs/math/0510327v2

Mathematics

Analysis of PDEs

119 pages

Scientific paper

With derive sharp spectral asymptotics (with the remainder estimate $O(\mu ^{-1}h^{1-d}+\mu ^{\frac{d} {2}-1}h^{1-\frac{d}{2}})$ for $d$-dimensional Schr\"odinger operator with a strong magnetic field; here $h$ and $\mu$ 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.

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