Eigenvalue bounds for two-dimensional magnetic Schroedinger operators
Spectral Theory
2011-09-07 v1 Mathematical Physics
math.MP
Abstract
We prove that the number of negative eigenvalues of two-dimensional magnetic Schroedinger operators is bounded from above by the strength of the corresponding electric potential. Such estimates fail in the absence of a magnetic field. We also show how the corresponding upper bounds depend on the properties of the magnetic field and discuss their connection with Hardy-type inequalities.
Cite
@article{arxiv.1103.5194,
title = {Eigenvalue bounds for two-dimensional magnetic Schroedinger operators},
author = {Hynek Kovarik},
journal= {arXiv preprint arXiv:1103.5194},
year = {2011}
}