Semiclassical asymptotics for a class of singular Schrödinger operators

Published 12 Oct 2020 in math.SP, math-ph, and math.MP | (2010.05417v1)

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

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