Displaced harmonic oscillator $V\sim \min \,[(x+d)^2,(x-d)^2]$ as a benchmark double-well quantum model
Mathematical Physics
2022-08-25 v2 math.MP
Abstract
For the displaced harmonic double-well oscillator the existence of exact polynomial bound states at certain displacements is revealed. The plets of these quasi-exactly solvable (QES) states are constructed in closed form. For non-QES states, Schr\"{o}dinger equation can still be considered ``non-polynomially exactly solvable'' (NES) because the exact left and right parts of the wave function (proportional to confluent hypergeometric function) just have to be matched in the origin.
Keywords
Cite
@article{arxiv.1607.01297,
title = {Displaced harmonic oscillator $V\sim \min \,[(x+d)^2,(x-d)^2]$ as a benchmark double-well quantum model},
author = {Miloslav Znojil},
journal= {arXiv preprint arXiv:1607.01297},
year = {2022}
}
Comments
21 pages, 3 figures