The singular harmonic oscillator revisited
Abstract
The one-dimensional Schr\"{o}dinger equation with the singular harmonic oscillator is investigated. The Hermiticity of the operators related to observable physical quantities is used as a criterion to show that the attractive or repulsive singular oscillator exhibits an infinite number of acceptable solutions provided the parameter responsible for the singularity is greater than a certain critical value, in disagreement with the literature. The problem for the whole line exhibits a two-fold degeneracy in the case of the singular oscillator, and the intrusion of additional solutions in the case of a nonsingular oscillator. Additionally, it is shown that the solution of the singular oscillator can not be obtained from the nonsingular oscillator via perturbation theory.
Cite
@article{arxiv.1304.0492,
title = {The singular harmonic oscillator revisited},
author = {Douglas R. M. Pimentel and Antonio S. de Castro},
journal= {arXiv preprint arXiv:1304.0492},
year = {2013}
}
Comments
15 pages, 4 figures, in Portuguese