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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.