Quantitative bounds versus existence of weakly coupled bound states for Schr\"odinger type operators
Mathematical Physics
2017-05-23 v2 math.MP
Abstract
It is well-known that for usual Schroedinger operators weakly coupled bound states exist in dimensions one and two, whereas in higher dimensions the famous Cwikel-Lieb-Rozenblum bound holds. We show for a large class of Schr\"odinger-type operators with general kinetic energies that these two phenomena are complementary. In particular, we explicitly get a natural semi-classical type bound on the number of bound states precisely in the situation when weakly coupled bound states exist not.
Keywords
Cite
@article{arxiv.1610.09891,
title = {Quantitative bounds versus existence of weakly coupled bound states for Schr\"odinger type operators},
author = {Vu Hoang and Dirk Hundertmark and Johanna Richter and Semjon Vugalter},
journal= {arXiv preprint arXiv:1610.09891},
year = {2017}
}