Semiclassical asymptotics for a class of singular Schrödinger operators

2020/10/12 by Rupert L. Frank, Frank, Rupert L., Simon Larson +1
Computer Science · Mathematics · #35P20 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2010.05417

openalex publication_date 2020/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ω⊂ ℝ^d be bounded with C¹ boundary. In this paper we consider Schrödinger operators -Δ+ W on Ω with W(x)\approxdist(x, ∂Ω)^-2 as dist(x, ∂Ω)→ 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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