On quantum waveguide with shrinking potential
Mathematical Physics
2015-05-14 v1 math.MP
Abstract
We consider the spectrum of a Schroedinger operator in a multi-dimensional cylinder perturbed by a shrinking potential. We study the phenomenon of a new eigenvalue emerging from the threshold of the essential spectrum and give the sufficient conditions for such eigenvalues to emerge. If such eigenvalues exist, we construct their asymptotic expansions.
Cite
@article{arxiv.0909.5115,
title = {On quantum waveguide with shrinking potential},
author = {A. Bikmetov and R. Gadyl'shin},
journal= {arXiv preprint arXiv:0909.5115},
year = {2015}
}