Inter-relations between additive shape invariant superpotentials

All known additive shape invariant superpotentials in nonrelativistic quantum mechanics belong to one of two categories: superpotentials that do not explicitly depend on h, and their h-dependent extensions. The former group themselves into two disjoint classes, depending on whether the corresponding Schrodinger 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 [19] 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. (C) 2019 Elsevier B.V. All rights reserved.