Eigenvalue asymptotics and exponential decay of eigenfunctions for Schrödinger operators with magnetic fields
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- by Zhongwei Shen
- Trans. Amer. Math. Soc. 348 (1996), 4465-4488
- DOI: https://doi.org/10.1090/S0002-9947-96-01709-6
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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.References
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Bibliographic Information
- Zhongwei Shen
- Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
- MR Author ID: 227185
- Email: shenz@ms.uky.edu
- Received by editor(s): May 19, 1995
- © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 348 (1996), 4465-4488
- MSC (1991): Primary 35P20, 35J10
- DOI: https://doi.org/10.1090/S0002-9947-96-01709-6
- MathSciNet review: 1370650