Counting Schr\"odinger boundstates: semiclassics and beyond
Spectral Theory
2008-11-22 v2
Abstract
This is a survey of the basic results on the behavior of the number of the eigenvalues of a Schr\"odinger operator, lying below its essential spectrum. We discuss both fast decaying potentials, for which this behavior is semiclassical, and slowly decaying potentials, for which the semiclassical rules are violated. Some new results are presented, concerning operators on product manifolds and graphs.
Cite
@article{arxiv.0803.3138,
title = {Counting Schr\"odinger boundstates: semiclassics and beyond},
author = {G. Rozenblum and M. Solomyak},
journal= {arXiv preprint arXiv:0803.3138},
year = {2008}
}
Comments
26 pages