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

Dyatlov, Semyon; Ghosh, Subhroshekhar

doi:10.1090/S0002-9939-2010-10519-1

Symmetry of bound and antibound states in the semiclassical limit for a general class of potentials
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by Semyon Dyatlov and Subhroshekhar Ghosh

Proc. Amer. Math. Soc. 138 (2010), 3203-3210

DOI: https://doi.org/10.1090/S0002-9939-2010-10519-1

Published electronically: May 14, 2010

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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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