Eigenvalue bounds for Schr\"odinger operators with complex potentials
Spectral Theory
2014-02-26 v1 Mathematical Physics
math.MP
Abstract
We show that the absolute values of non-positive eigenvalues of Schr\"odinger operators with complex potentials can be bounded in terms of L_p-norms of the potential. This extends an inequality of Abramov, Aslanyan, and Davies to higher dimensions and proves a conjecture by Laptev and Safronov. Our main ingredient are the uniform Sobolev inequalities of Kenig, Ruiz, and Sogge.
Cite
@article{arxiv.1005.2785,
title = {Eigenvalue bounds for Schr\"odinger operators with complex potentials},
author = {Rupert L. Frank},
journal= {arXiv preprint arXiv:1005.2785},
year = {2014}
}
Comments
7 pages