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Eigenvalue asymptotics and exponential decay of eigenfunctions for Schrödinger operators with magnetic fields
Authors:Zhongwei Shen
Affiliation:Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Abstract:We consider the Schrödinger operator with magnetic field,

begin{equation*}H=(frac {1}{i}nabla -{overset {rightharpoonup }{a}}(x))^{2}+V(x)  text { in } mathbb {R}^{n}. end{equation*}

Assuming that $Vge 0$ and $|text {curl}, overset {rightharpoonup }{a}|+V+1$ is locally in certain reverse Hölder class, we study the eigenvalue asymptotics and exponential decay of eigenfunctions.

Keywords:Eigenvalue asymptotics, Schrö  dinger operator, reverse Hö  lder class
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