Inter-Relations of Solvable Potentials

Asim Gangopadhyaya; Prasanta K. Panigrahi; Uday P. Sukhatne

doi:10.5169/seals-116652

Inter-Relations of Solvable Potentials

Asim Gangopadhyaya, Prasanta K. Panigrahi, Uday P. Sukhatne

Department of Physics

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

Abstract

Solvable Natanzon potentials in nonrelativistic quantum mechanics are known to group into two disjoint classes depending on whether the Schrödinger equation can be reduced to a hypergeometric or a confluent hypergeometric equation. All the potentials within each class are connected via point canonical transformations. We establish a connection between the two classes with appropriate limiting procedures and redefinition of parameters, thereby inter-relating all known solvable potentials.

Original language	American English
Journal	Physics: Faculty Publications and Other Works
Volume	67
Issue number	4
DOIs	https://doi.org/10.5169/seals-116652
State	Published - Jul 1 1994

Keywords

quantum mechanics

Disciplines

Physics

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title = "Inter-Relations of Solvable Potentials",

abstract = " Solvable Natanzon potentials in nonrelativistic quantum mechanics are known to group into two disjoint classes depending on whether the Schr{\"o}dinger equation can be reduced to a hypergeometric or a confluent hypergeometric equation. All the potentials within each class are connected via point canonical transformations. We establish a connection between the two classes with appropriate limiting procedures and redefinition of parameters, thereby inter-relating all known solvable potentials.",

keywords = "quantum mechanics",

author = "Asim Gangopadhyaya and Panigrahi, {Prasanta K.} and Sukhatne, {Uday P.}",

year = "1994",

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AU - Gangopadhyaya, Asim

AU - Panigrahi, Prasanta K.

AU - Sukhatne, Uday P.

PY - 1994/7/1

Y1 - 1994/7/1

N2 - Solvable Natanzon potentials in nonrelativistic quantum mechanics are known to group into two disjoint classes depending on whether the Schrödinger equation can be reduced to a hypergeometric or a confluent hypergeometric equation. All the potentials within each class are connected via point canonical transformations. We establish a connection between the two classes with appropriate limiting procedures and redefinition of parameters, thereby inter-relating all known solvable potentials.

AB - Solvable Natanzon potentials in nonrelativistic quantum mechanics are known to group into two disjoint classes depending on whether the Schrödinger equation can be reduced to a hypergeometric or a confluent hypergeometric equation. All the potentials within each class are connected via point canonical transformations. We establish a connection between the two classes with appropriate limiting procedures and redefinition of parameters, thereby inter-relating all known solvable potentials.

KW - quantum mechanics

UR - https://ecommons.luc.edu/physics_facpubs/10

U2 - 10.5169/seals-116652

DO - 10.5169/seals-116652

M3 - Article

VL - 67

JO - Physics: Faculty Publications and Other Works

JF - Physics: Faculty Publications and Other Works

IS - 4

ER -

Inter-Relations of Solvable Potentials

Abstract

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