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Proceedings of the American Mathematical Society

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Symmetry of bound and antibound states in the semiclassical limit for a general class of potentials


Authors: Semyon Dyatlov and Subhroshekhar Ghosh
Journal: Proc. Amer. Math. Soc. 138 (2010), 3203-3210
MSC (2010): Primary 34L25; Secondary 65L15, 81U20
Published electronically: May 14, 2010
MathSciNet review: 2653945
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Abstract: We consider the Schrödinger operator $ -h^2\partial_x^2+V(x)$ on a half-line, where $ V$ is a compactly supported potential which is positive near the endpoint of its support. We prove that the eigenvalues and the purely imaginary resonances are symmetric up to an error $ Ce^{-\delta/h}$.


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Additional Information

Semyon Dyatlov
Affiliation: Department of Mathematics, Evans Hall, University of California, Berkeley, California 94720
Email: dyatlov@math.berkeley.edu

Subhroshekhar Ghosh
Affiliation: Department of Mathematics, Evans Hall, University of California, Berkeley, California 94720
Email: subhro@math.berkeley.edu

DOI: https://doi.org/10.1090/S0002-9939-2010-10519-1
Received by editor(s): December 2, 2009
Published electronically: May 14, 2010
Communicated by: Hart F. Smith
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.