Quantum Systems at The Brink
Mathematical Physics
2024-10-22 v1 math.MP
Abstract
We present a method to calculate the asymptotic behavior of eigenfunctions of Schr\"odinger operators that also works at the threshold of the essential spectrum. It can be viewed as a higher order correction to the well-known WKB method which does need a safety distance to the essential spectrum. We illustrate its usefulness on examples of quantum particles in a potential well with a long-range repulsive term outside the well.
Cite
@article{arxiv.2210.16356,
title = {Quantum Systems at The Brink},
author = {Dirk Hundertmark and Michal Jex and Markus Lange},
journal= {arXiv preprint arXiv:2210.16356},
year = {2024}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2012.12748