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Exactness Of Swkb For Shape Invariant Potentials, Asim Gangopadhyaya, Jeffry V. Mallow, Emeritus, Constantin Rasinariu, Jonathan Bougie
Exactness Of Swkb For Shape Invariant Potentials, Asim Gangopadhyaya, Jeffry V. Mallow, Emeritus, Constantin Rasinariu, Jonathan Bougie
Physics: Faculty Publications and Other Works
The supersymmetry-based semiclassical method (SWKB) is known to produce exact spectra for conventional shape invariant potentials. In this paper we prove that this exactness follows from their additive shape invariance.
Inter-Relations Between Additive Shape Invariant Superpotentials, Jeffry V. Mallow, Emeritus, Asim Gangopadhyaya, Jonathan Bougie, Constantin Rasinariu
Inter-Relations Between Additive Shape Invariant Superpotentials, Jeffry V. Mallow, Emeritus, Asim Gangopadhyaya, Jonathan Bougie, Constantin Rasinariu
Physics: Faculty Publications and Other Works
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 [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 …