Lieb-Thirring inequalities for geometrically induced bound states
Mathematical Physics
2020-02-03 v1 Mesoscale and Nanoscale Physics
math.MP
Quantum Physics
Abstract
We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schr\"odinger operators in wave guides with local perturbations. The estimates are optimal in the weak-coupling case. To illustrate their applications, we consider, in particular, a straight strip and a straight circular tube with either mixed boundary conditions or boundary deformations.
Keywords
Cite
@article{arxiv.math-ph/0405046,
title = {Lieb-Thirring inequalities for geometrically induced bound states},
author = {Pavel Exner and Helmut Linde and Timo Weidl},
journal= {arXiv preprint arXiv:math-ph/0405046},
year = {2020}
}
Comments
LaTeX2e, 14 pages