Semiclassical asymptotics for a class of singular Schrödinger operators

  • Rupert L. Frank

    Ludwig-Maximilians-Universität München, Germany; California Institute of Technology Pasadena, USA
  • Simon Larson

    California Institute of Technology, Pasadena, USA
Semiclassical asymptotics for a class of singular Schrödinger operators cover
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Abstract

Let ΩRd\Omega \subset \mathbb{R}^d be bounded with C1C^1 boundary. In this paper we consider Schrödinger operators Δ+W-\Delta+ W on Ω\Omega with W(x)dist(x,Ω)2W(x)\approx\operatorname{dist}(x, \partial\Omega)^{-2} as dist(x,Ω)0\operatorname{dist}(x, \partial\Omega)\to 0. Under weak assumptions on WW we derive a two-term asymptotic formula for the sum of the eigenvalues of such operators.