Counting Schrödinger Boundstates: Semiclassics and Beyond

  • Grigori Rozenblum
  • Michael Solomyak
Part of the International Mathematical Series book series (IMAT, volume 9)


This is a survey of the basic results on the behavior of the num ber 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.


Quadratic Form Potential Versus Heat Kernel Asymptotic Formula Essential Spectrum 
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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Chalmers University of Technology and The University of GothenburgGothenburgSweden
  2. 2.The Weizmann Institute of Science RehovotIsrael

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