On the negative spectrum of two-dimensional Schrödinger operators with radial potentials

Ari Laptev; Michael Solomyak

doi:10.1007/s00220-012-1501-4

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arXiv · 1108.1002

On the negative spectrum of two-dimensional Schrödinger operators with radial potentials

Ari Laptev·Michael Solomyak

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Abstract

For a two-dimensional Schrödinger operator $H_{αV}=-Δ-αV$ with the radial potential $V(x)=F(|x|), F(r)\ge 0$, we study the behavior of the number $N_-(H_{αV})$ of its negative eigenvalues, as the coupling parameter $α$ tends to infinity. We obtain the necessary and sufficient conditions for the semi-classical growth $N_-(H_{αV})=O(α)$ and for the validity of the Weyl asymptotic law.

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BibTeX RIS

Ari Laptev, Michael Solomyak. 2011-12-21. On the negative spectrum of two-dimensional Schrödinger operators with radial potentials. https://doi.org/10.1007/s00220-012-1501-4

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