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Douglas R. M. Pimentel

Publications and source records attributed to Douglas R. M. Pimentel.

3 recordsLinked to original sources
arXiv2013

A brief discussion on the possible bound states for a class of singular potentials

The one-dimensional Schrödinger equation for a class of potentials $V(|x|)$ which vanish at infinity and present dominant singularity at the origin in the form $α/|x|^β$ ($0<β\leq 2$) is investigated. The Hermiticity of the operators related to observable physical quantities is used to determinate the proper boundary conditions. Double degeneracy and exclusion of symmetric solutions, consonant the value of $β$, are discussed. Explicit solutions for the hydrogen atom and the Kratzer potential are presented.

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arXiv2013

The singular harmonic oscillator revisited

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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