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arXiv · 1909.02704

Inter-relations between additive shape invariant superpotentials

Jeffry V. Mallow·Asim Gangopadhyaya·Jonathan Bougie·Constantin Rasinariu
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Abstract

All known additive shape invariant superpotentials in nonrelativistic quantum mechanics belong to one of two categories: superpotentials that do not explicitly depend on $\hbar$, and their $\hbar$-dependent extensions. The former group themselves into two disjoint classes, depending on whether the corresponding Schrödinger equation can be reduced to a hypergeometric equation (type-I) or a confluent hypergeometric equation (type-II). All the superpotentials within each class are connected via point canonical transformations. Previous work showed that type-I superpotentials produce type-II via limiting procedures. In this paper we develop a method to generate a type I superpotential from type II, thus providing a pathway to interconnect all known additive shape invariant superpotentials.

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Jeffry V. Mallow, Asim Gangopadhyaya, Jonathan Bougie, Constantin Rasinariu. 2019-11-21. Inter-relations between additive shape invariant superpotentials. https://doi.org/10.1016/j.physleta.2019.126129

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