Summation formula inequalities for eigenvalues of the perturbed harmonic oscillator
Spectral Theory
2016-05-09 v1
Abstract
We derive explicit inequalities for sums of eigenvalues of one-dimensional Schr\"{o}dinger operators on the whole line. In the case of the perturbed harmonic oscillator, these bounds converge to the corresponding trace formula in the limit as the number of eigenvalues covers the whole spectrum.
Keywords
Cite
@article{arxiv.1605.01928,
title = {Summation formula inequalities for eigenvalues of the perturbed harmonic oscillator},
author = {Pedro Freitas and James B. Kennedy},
journal= {arXiv preprint arXiv:1605.01928},
year = {2016}
}
Comments
15 pages, to appear in Osaka J. Math