On Solvable Potentials, Supersymmetry, and the One-Dimensional Hydrogen Atom

R. P. Martínez-y-Romero, H. N. Núnez-Yépez, A. L. Salas-Brito

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DOI: 10.4236/cn.2010.21009                

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.

Keywords

one-dimensional hydrogen atom, one-dimensional Coulomb potential, supersymmetric quantum mechanics.

Conflicts of Interest

The authors declare no conflicts of interest.

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