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

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Abstract

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