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Eigenvalue Asymptotics and Exponential Decay of Eigenfunctions for Schrödinger Operators with Magnetic Fields

Zhongwei Shen
Transactions of the American Mathematical Society
Vol. 348, No. 11 (Nov., 1996), pp. 4465-4488
Stable URL: http://www.jstor.org/stable/2155428
Page Count: 24
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Eigenvalue Asymptotics and Exponential Decay of Eigenfunctions for Schrödinger Operators with Magnetic Fields
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Abstract

We consider the Schrödinger operator with magnetic field, $H=(\frac{1}{i}\nabla -**??**(x))^{2}+V(x)\quad \text{in}\ {\Bbb R}^{n}$. Assuming that V ≥ 0 and $|{\rm curl}**??**|+V+1$ is locally in certain reverse Hölder class, we study the eigenvalue asymptotics and exponential decay of eigenfunctions.

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