A Schr\"odinger operator with confining potential having quadratic growth
Analysis of PDEs
2025-05-19 v1 Spectral Theory
Abstract
We study the spectral properties of a Schr\"odinger operator, in presence of a confining potential given by the distance squared from a fixed compact potential well. We prove continuity estimates on both the eigenvalues and the eigenstates, lower bounds on the ground state energy, regularity and integrability properties of eigenstates. We also get explicit decay estimates at infinity, by means of elementary nonlinear methods.
Cite
@article{arxiv.2505.11113,
title = {A Schr\"odinger operator with confining potential having quadratic growth},
author = {Chiara Alessi and Lorenzo Brasco and Michele Miranda},
journal= {arXiv preprint arXiv:2505.11113},
year = {2025}
}
Comments
36 pages, to appear on Anal. Math. Phys