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

Semyon Dyatlov; Subhroshekhar Ghosh

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

paper

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

arXiv:0911.4282 · doi:10.1090/S0002-9939-2010-10519-1

Abstract

We consider the semiclassical 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 $C e^{- δ / h}$ .

arXiv comment10 pages, 1 figure