Bound on the number of negative eigenvalues of two-dimensional Schr\"odinger operators on domains

Rupert L. Frank; Ari Laptev

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arXiv · 1712.03167

Bound on the number of negative eigenvalues of two-dimensional Schr\"odinger operators on domains

Rupert L. Frank·Ari Laptev

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Abstract

A fundamental result of Solomyak says that the number of negative eigenvalues of a Schr\"odinger operator on a two-dimensional domain is bounded from above by a constant times a certain Orlicz norm of the potential. Here we show that in the case of Dirichlet boundary conditions the constant in this bound can be chosen independently of the domain.

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BibTeX RIS

Rupert L. Frank, Ari Laptev. 2017-12-08. Bound on the number of negative eigenvalues of two-dimensional Schr\"odinger operators on domains. https://arxiv.org/abs/1712.03167

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