O oscilador harmônico singular revisitado

• Main Author: Pimentel, Douglas Roberto de Matos [UNESP]
• Publication Date: 2013
• Other Authors: Castro, Antonio Soares de [UNESP]
• Format: Article
• Language: por
• Source: Repositório Institucional da UNESP
• Download full: http://dx.doi.org/10.1590/S1806-11172013000300003; http://hdl.handle.net/11449/109657
• topic: oscilador harmônico; potencial singular; degenerescência; colapso para o centro; harmonic oscillator; singular potential; degeneracy; collapse to the center

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.