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Zbl 0849.34069
Gangopadhyaya, Asim; Panigrahi, Prasanta K.; Sukhatme, Uday P.
Inter-relations of solvable potentials. (English)
[J] Helv. Phys. Acta 67, No.4, 363-368 (1994). ISSN 0018-0238

Summary: 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.

MSC 2000:: *34L40 Particular ordinary differential operators
81Q05 Closed and approximate solutions to quantum-mechanical equations

Keywords: solvable Natanzon potentials; Schrödinger equation; confluent hypergeometric equation; canonical transformations

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