Physics Letters A
All known additive shape invariant superpotentials in nonrelativistic quantum mechanics belong to one of two categories: superpotentials that do not explicitly depend on ħ, and their ħ-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.
Mallow,, Jeffry V. Emeritus; Gangopadhyaya, Asim; Bougie, Jonathan; and Rasinariu, Constantin, "Inter-relations Between Additive Shape Invariant Superpotentials" (2020). Physics: Faculty Publications and Other Works. 61.
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© Elsevier B.V., 2020.
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