Generation of a Novel Exactly Solvable Potential

Abstract

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 $\hbar$ is complete. Additionally, a set of "extended" superpotentials has been identified, each containing a conventional superpotential as a kernel and additional $\hbar$-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.