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.
Highlights
A paper of Morales et al [1] has discussed the use of supersymmetric and shape invariance techniques and of Darboux and intertwining transformations, for building new solvable potentials
The ways for improving on techniques for finding new solvable potentials based on supersymmetry and shape invariance has been discussed by Morales et al
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
Summary
A paper of Morales et al [1] has discussed the use of supersymmetric and shape invariance techniques and of Darboux and intertwining transformations, for building new solvable potentials. 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. To illustrate these ideas they apply them to hydrogen-like potentials and to radial and one-dimensional problems.
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