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Asymptotics of the negative discrete spectrum of a class of Schrödinger operators with large coupling constant


Author: Ari Laptev
Journal: Proc. Amer. Math. Soc. 119 (1993), 481-488
MSC: Primary 35P20; Secondary 35J10, 47F05
MathSciNet review: 1149974
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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 \notin {L_{m/2}}({R^m}),\;m \geqslant 3$. The result is very sensitive to small perturbations of the potential and depends on the negative spectrum of some auxiliary differential problems on $ {S^{m - 1}}$.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1149974-0
Article copyright: © Copyright 1993 American Mathematical Society