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arXiv · 1304.0492

The singular harmonic oscillator revisited

Douglas R. M. Pimentel·Antonio S. de Castro
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Abstract

The one-dimensional Schrödinger 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.

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Douglas R. M. Pimentel, Antonio S. de Castro. 2013-04-01. The singular harmonic oscillator revisited. https://arxiv.org/abs/1304.0492

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