Wednesday, April 3, 2013

1304.0492 (Douglas R. M. Pimentel et al.)

The singular harmonic oscillator revisited    [PDF]

Douglas R. M. Pimentel, Antonio S. de Castro
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.
View original: http://arxiv.org/abs/1304.0492

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