## A brief discussion on the possible bound states for a class of singular potentials    [PDF]

Douglas R. M. Pimentel, Antonio S. de Castro
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.
View original: http://arxiv.org/abs/1308.0030