arXiv Open Access 2011

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

Ari Laptev Michael Solomyak

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Abstrak

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.

Topik & Kata Kunci

math.SP

Penulis (2)

Ari Laptev

Michael Solomyak

Format Sitasi

APA MLA BibTeX

Laptev, A., Solomyak, M. (2011). On the negative spectrum of two-dimensional Schrödinger operators with radial potentials. https://arxiv.org/abs/1108.1002

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2011
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓