Bound on the number of negative eigenvalues of two-dimensional Schrödinger operators on domains

Abstract

A fundamental result of Solomyak says that the number of negative eigenvalues of a Schrödinger 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.

arXiv comment17 pages; Dedicated to the memory of M. Z. Solomyak