Sharp Spectral Asymptotics for Magnetic Schrödinger Operator with Irregular Potential

Details Sharp Spectral Asymptotics for Magnetic Schrödinger Operator with Irregular Potential Sharp Spectral Asymptotics for Magnetic Schrödinger Operator with Irregular Potential

2006-03-05

arxiv.org/abs/math/0603119v1

Russian Journal of Mathematical Physics, 11:4 (2004), 415-428

Mathematics

Analysis of PDEs

Scientific paper

Survey: In this paper I consider sharp spectral asymptotics for multidimensional magnetic Schr\"odinger operator with irregular coefficients with respect to two parameters -- semiclassical parameter $h$ and coupling parameter $\mu$. There are few principally different cases, depending on dimension, rank of magnetic intensity matrix, relation between $h$ and $\mu$ and some extra assumptions.

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