On the spectrum of a Schroedinger operator perturbed by a fast oscillating potential
Abstract
We study the spectrum of a onedimensional 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2005
 DOI:
 10.48550/arXiv.mathph/0505068
 arXiv:
 arXiv:mathph/0505068
 Bibcode:
 2005math.ph...5068B
 Keywords:

 Mathematical Physics;
 Mathematics  Mathematical Physics
 EPrint:
 The article is written originally in Russian. Translation is made by the author. In the present version several typos occured in the previous one were corrected