On the spectrum of the Schrödinger operator perturbed by a rapidly oscillating potential |
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Authors: | D. I. Borisov |
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Affiliation: | (1) Bashkir State Pedagogical University, Russia;(2) Nuclear Physics Institute of CzAS, Czech Republic |
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Abstract: | We study the spectrum of the one-dimensional Schrödinger operator perturbed by a rapidly oscillating potential. The oscillation period is a small parameter. We find explicitly the essential spectrum and study the existence of the discrete spectrum. Complete asymptotic expansions of the eigenvalues and corresponding eigenfunctions are constructed. |
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