On the spectrum of a Schroedinger operator perturbed by a fast oscillating potential

Details On the spectrum of a Schroedinger operator perturbed by a fast oscillating potential On the spectrum of a Schroedinger operator perturbed by a fast oscillating potential

2005-05-25

arxiv.org/abs/math-ph/0505068v2

Journal of Mathematical Sciences. 2006. V. 139. No. 1. P. 6243-6322.

Physics

Mathematical Physics

The article is written originally in Russian. Translation is made by the author. In the present version several typos occured

Scientific paper

We study the spectrum of a one-dimensional Schroedinger operator perturbed by
a fast oscillating potential. The oscillation period is a small parameter. The
essential spectrum is found in an explicit form. The existence and multiplicity
of the discrete spectrum are studied. The complete asymptotics expansions for
the eigenvalues and the associated eigenfunctions are constructed.

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