O oscilador harmônico singular revisitado

• Autor(a) principal: Pimentel, Douglas R.M. [UNESP]
• Data de Publicação: 2013
• Outros Autores: de Castro, Antonio S. [UNESP]
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: 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.