We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schrödinger 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.
%0 Journal Article
%1 MR2107707
%A Exner, Pavel
%A Linde, Helmut
%A Weidl, Timo
%D 2004
%J Lett. Math. Phys.
%K Weidl bound geometrically induced states
%N 1
%P 83--95
%R 10.1007/s11005-004-1741-0
%T Lieb-Thirring inequalities for geometrically induced bound states
%U https://doi.org/10.1007/s11005-004-1741-0
%V 70
%X We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schrödinger 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.
@article{MR2107707,
abstract = {We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schrödinger 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.},
added-at = {2022-03-30T16:32:23.000+0200},
author = {Exner, Pavel and Linde, Helmut and Weidl, Timo},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/21644660b6e0b2bd03210c20cf3c1e752/elkepeter},
doi = {10.1007/s11005-004-1741-0},
interhash = {ae68a2a393315d8acefd999fc3bbfb41},
intrahash = {1644660b6e0b2bd03210c20cf3c1e752},
issn = {0377-9017},
journal = {Lett. Math. Phys.},
keywords = {Weidl bound geometrically induced states},
mrclass = {81Q10 (35J10 35P15)},
mrnumber = {2107707},
mrreviewer = {G\"{u}nter Berger},
number = 1,
pages = {83--95},
timestamp = {2023-04-21T12:45:24.000+0200},
title = {Lieb-{T}hirring inequalities for geometrically induced bound states},
url = {https://doi.org/10.1007/s11005-004-1741-0},
volume = 70,
year = 2004
}