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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Eigenvalue asymptotics and exponential decay
of eigenfunctions for Schrödinger operators
with magnetic fields


Author: Zhongwei Shen
Journal: Trans. Amer. Math. Soc. 348 (1996), 4465-4488
MSC (1991): Primary 35P20, 35J10
MathSciNet review: 1370650
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Abstract | References | Similar Articles | Additional Information

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 $V\ge 0$ 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.


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Additional Information

Zhongwei Shen
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: shenz@ms.uky.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01709-6
PII: S 0002-9947(96)01709-6
Keywords: Eigenvalue asymptotics, Schrödinger operator, reverse Hölder class
Received by editor(s): May 19, 1995
Article copyright: © Copyright 1996 American Mathematical Society