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Inter-Relations Of Solvable Potentials, Asim Gangopadhyaya, Prasanta K. Panigrahi, Uday P. Sukhatne

Physics: Faculty Publications and Other Works

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.