Counting Schrödinger boundstates: semiclassics and beyond

Details Counting Schrödinger boundstates: semiclassics and beyond Counting Schrödinger boundstates: semiclassics and beyond

2008-03-21

arxiv.org/abs/0803.3138v2

Mathematics

Spectral Theory

26 pages

Scientific paper

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.

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