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Asymptotics of the Negative Discrete Spectrum of a Class of Schrödinger Operators with Large Coupling Constant

Ari Laptev
Proceedings of the American Mathematical Society
Vol. 119, No. 2 (Oct., 1993), pp. 481-488
DOI: 10.2307/2159932
Stable URL: http://www.jstor.org/stable/2159932
Page Count: 8
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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.
Asymptotics of the Negative Discrete Spectrum of a Class of Schrödinger Operators with Large Coupling Constant
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Abstract

We obtain the asymptotics of the negative discrete spectrum of the Schrödinger operator with a large coupling constant and potentials $V \not\in L_{m/2}(R^m), m \geq 3$. The result is very sensitive to small perturbations of the potential and depends on the negative spectrum of some auxiliary differential problems on Sm - 1.

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