Abstract
For a two-dimensional Schrödinger operator H α V = −Δ −αV with the radial potential V(x) = F(|x|), F(r) ≥ 0, we study the behavior of the number N −(H α V ) 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 α V ) = O(α) and for the validity of the Weyl asymptotic law.
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Laptev, A., Solomyak, M. On the Negative Spectrum of the Two-Dimensional Schrödinger Operator with Radial Potential. Commun. Math. Phys. 314, 229–241 (2012). https://doi.org/10.1007/s00220-012-1501-4
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DOI: https://doi.org/10.1007/s00220-012-1501-4