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

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

2011-08-04

arxiv.org/abs/1108.1002v3

Mathematics

Spectral Theory

13 pages

Scientific paper

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

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