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arXiv · 1506.08809

Generation of a Novel Exactly Solvable Potential

Jonathan Bougie·Asim Gangopadhyaya·Jeffry V. Mallow·Constantin Rasinariu
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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.

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Jonathan Bougie, Asim Gangopadhyaya, Jeffry V. Mallow, Constantin Rasinariu. 2015-06-29. Generation of a Novel Exactly Solvable Potential. https://doi.org/10.1016/j.physleta.2015.06.058

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