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arXiv · 0911.4282

Symmetry of Bound and Antibound States in the Semiclassical Limit for a General Class of Potentials

Semyon Dyatlov·Subhroshekhar Ghosh
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Abstract

We consider the semiclassical Schr\"odinger 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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Semyon Dyatlov, Subhroshekhar Ghosh. 2009-11-22. Symmetry of Bound and Antibound States in the Semiclassical Limit for a General Class of Potentials. https://doi.org/10.1090/s0002-9939-2010-10519-1

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