O oscilador harmônico singular revisitado

• Main Author: Pimentel, Douglas R.M. [UNESP]
• Publication Date: 2013
• Other Authors: de Castro, Antonio S. [UNESP]
• Format: Article
• Language: por
• Source: Repositório Institucional da UNESP
• Download full: http://hdl.handle.net/11449/227218
• topic: Collapse to the center; Degeneracy; Harmonic oscillator; Singular potential

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. © The Sociedade Brasileira de Física.