Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physics
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 …
Generation Of A Novel Exactly Solvable Potential, Jonathan Bougie, Asim Gangopadhyaya, Jeffry V. Mallow, Emeritus, Constantin Rasinariu
Generation Of A Novel Exactly Solvable Potential, Jonathan Bougie, Asim Gangopadhyaya, Jeffry V. Mallow, Emeritus, Constantin Rasinariu
Physics: Faculty Publications and Other Works
We report a new shape-invariant (SI) isospectral extension of the Morse potential. Previous investigations have shown that the list of “conventional” SI superpotentials that do not depend explicitly on Planck's constant ħ is complete. Additionally, a set of “extended” superpotentials has been identified, each containing a conventional superpotential as a kernel and additional ħ-dependent terms. We use the partial differential equations satisfied by all SI superpotentials to find a SI extension of Morse with novel properties. It has the same eigenenergies as Morse but different asymptotic limits, and does not conform to the standard generating structure for isospectral deformations.