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

Douglas R. M. Pimentel; Antonio S. de Castro

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

Quantum Physics 2013-08-02 v1

Authors: Douglas R. M. Pimentel , Antonio S. de Castro

Abstract

The one-dimensional Schr\"{o}dinger equation for a class of potentials $V(|x|)$ which vanish at infinity and present dominant singularity at the origin in the form $\alpha /|x|^{\beta}$ ( $0<\beta \leq 2$ ) 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 $\beta$ , are discussed. Explicit solutions for the hydrogen atom and the Kratzer potential are presented.

Keywords

singular potentials Schrödinger equation bound states Hermiticity boundary conditions hydrogen atom Kratzer potential

Cite

@article{arxiv.1308.0030,
  title  = {A brief discussion on the possible bound states for a class of singular potentials},
  author = {Douglas R. M. Pimentel and Antonio S. de Castro},
  journal= {arXiv preprint arXiv:1308.0030},
  year   = {2013}
}

Comments

16 pages, 2 figures, in Portuguese. arXiv admin note: text overlap with arXiv:1304.0492

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

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