English

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

R2 v1 2026-07-22T16:24:29.213Z