TITLE:
On Solvable Potentials, Supersymmetry, and the One-Dimensional Hydrogen Atom
AUTHORS:
R. P. Martínez-y-Romero, H. N. Núnez-Yépez, A. L. Salas-Brito
KEYWORDS:
one-dimensional hydrogen atom, one-dimensional Coulomb potential, supersymmetric quantum mechanics.
JOURNAL NAME:
Communications and Network,
Vol.2 No.1,
March
1,
2010
ABSTRACT: The ways for improving on techniques for finding new solvable potentials based on supersymmetry and shape invariance has been discussed by Morales et al. [1] In doing so they address the peculiar system known as the one-dimensional hydrogen atom. In this paper we show that their remarks on such problem are mistaken. We do this by explicitly constructing both the one-dimensional Coulomb potential and the superpotential associated with the problem, objects whose existence are denied in the mentioned paper.