Inter-relations Between Additive Shape Invariant Superpotentials
Item
Title
Inter-relations Between Additive Shape Invariant Superpotentials
List of Authors
Jeffry V.Mallow; Asim Gangopadhyaya; Jonathan Bougie; Constantin Rasinariu
Abstract
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.
Date
2020
Publication Title
Physics Letters A
Publisher
Elsevier
Identifier
DOI 10.1016/j.physleta.2019.126129
Bibliographic Citation
Mallow, Jeffry V.; Asim Gangopadhyaya; Jonathan Bougie; Constantin Rasinariu. (2020) "Inter-relations Between Additive Shape Invariant Superpotentials" 384(6).
