Inter-relations Between Additive Shape Invariant Superpotentials

Jeffry V. Mallow,; Asim Gangopadhyaya; Jonathan Bougie; Constantin Rasinariu

doi:10.1016/j.physleta.2019.126129

Inter-relations Between Additive Shape Invariant Superpotentials

Jeffry V. Mallow,, Asim Gangopadhyaya, Jonathan Bougie, Constantin Rasinariu

Department of Physics

Loyola University Chicago

Research output: Contribution to journal › Article › peer-review

Abstract

All known additive shape invariant superpotentials in nonrelativistic quantum mechanics belong to one of two categories: superpotentials that do not explicitly depend on &hstrok; , and their &hstrok; -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 <a href="https://www-sciencedirect-com.flagship.luc.edu/science/article/abs/pii/S0375960119310473#br0190"> </a> [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.

Original language	American English
Journal	Physics: Faculty Publications and Other Works
Volume	384
Issue number	6
DOIs	https://doi.org/10.1016/j.physleta.2019.126129
State	Published - Feb 28 2020

Keywords

Supersymmetric quantum mechanics
Shape invariance
Exactly solvable systems
Extended potentials
Point canonical transformations
Isospectral deformation

Disciplines

Physics
Applied Mathematics
Quantum Physics

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title = "Inter-relations Between Additive Shape Invariant Superpotentials",

abstract = " All known additive shape invariant superpotentials in nonrelativistic quantum mechanics belong to one of two categories: superpotentials that do not explicitly depend on &hstrok; , and their &hstrok; -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 [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.",

keywords = "Supersymmetric quantum mechanics, Shape invariance, Exactly solvable systems, Extended potentials, Point canonical transformations, Isospectral deformation",

author = "Mallow,, {Jeffry V.} and Asim Gangopadhyaya and Jonathan Bougie and Constantin Rasinariu",

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T1 - Inter-relations Between Additive Shape Invariant Superpotentials

AU - Mallow,, Jeffry V.

AU - Gangopadhyaya, Asim

AU - Bougie, Jonathan

AU - Rasinariu, Constantin

PY - 2020/2/28

Y1 - 2020/2/28

N2 - All known additive shape invariant superpotentials in nonrelativistic quantum mechanics belong to one of two categories: superpotentials that do not explicitly depend on &hstrok; , and their &hstrok; -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 [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.

AB - All known additive shape invariant superpotentials in nonrelativistic quantum mechanics belong to one of two categories: superpotentials that do not explicitly depend on &hstrok; , and their &hstrok; -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 [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.

KW - Supersymmetric quantum mechanics

KW - Shape invariance

KW - Exactly solvable systems

KW - Extended potentials

KW - Point canonical transformations

KW - Isospectral deformation

UR - https://ecommons.luc.edu/physics_facpubs/61

UR - https://www.sciencedirect.com/science/article/pii/S0375960119310473

U2 - 10.1016/j.physleta.2019.126129

DO - 10.1016/j.physleta.2019.126129

M3 - Article

VL - 384

JO - Physics: Faculty Publications and Other Works

JF - Physics: Faculty Publications and Other Works

IS - 6

ER -

Inter-relations Between Additive Shape Invariant Superpotentials

Abstract

Keywords

Disciplines

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