Counting Schrödinger boundstates: semiclassics and beyond
Abstract
Description
This is a survey of the basic results on the behavior of the number of the eigenvalues of a Schrödinger 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.
26 pages
26 pages