Weak coupling limit for Schr\"odinger-type operators with degenerate kinetic energy for a large class of potentials
Abstract
We improve results by Frank, Hainzl, Naboko, and Seiringer [12] and Hainzl and Seiringer [20] on the weak coupling limit of eigenvalues for Schr\"odinger-type operators whose kinetic energy vanishes on a codimension one submanifold. The main technical innovation that allows us to go beyond the potentials considered in [12, 20] is the use of the Tomas-Stein theorem.
Keywords
Cite
@article{arxiv.2006.07110,
title = {Weak coupling limit for Schr\"odinger-type operators with degenerate kinetic energy for a large class of potentials},
author = {Jean-Claude Cuenin and Konstantin Merz},
journal= {arXiv preprint arXiv:2006.07110},
year = {2023}
}
Comments
27 pages. Title changed, corrected misprints, included further details in some proofs, carried out some extensions of the main result (more general kinetic energies, second order in the asymptotics, improvements for potentials with further symmetries). This is a preprint of an article published in Letters in Mathematical Physics, available online at https://doi.org/10.1007/s11005-021-01385-2