# 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

A subscription is required to access this book chapter.

## Abstract

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