Semiclassical asymptotics for a class of singular Schrödinger operators
Let $Ω\subset \mathbb{R}^d$ be bounded with $C^1$ boundary. In this paper we consider Schrödinger operators $-Δ+ W$ on $Ω$ with $W(x)\approx\mathrm{dist}(x, \partialΩ)^{-2}$ as $\mathrm{dist}(x, \partialΩ)\to 0$. Under weak assumptions on $W$ we derive a two-term asymptotic formula for the sum of th...
| Main Authors: | , |
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| Format: | Article in Journal/Newspaper |
| Language: | unknown |
| Published: |
arXiv
2020
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| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.2010.05417 https://arxiv.org/abs/2010.05417 |
| Summary: | Let $Ω\subset \mathbb{R}^d$ be bounded with $C^1$ boundary. In this paper we consider Schrödinger operators $-Δ+ W$ on $Ω$ with $W(x)\approx\mathrm{dist}(x, \partialΩ)^{-2}$ as $\mathrm{dist}(x, \partialΩ)\to 0$. Under weak assumptions on $W$ we derive a two-term asymptotic formula for the sum of the eigenvalues of such operators. : Dedicated to Ari Laptev on the occasion of his 70th birthday |
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