Article ID Journal Published Year Pages File Type
1859613 Physics Letters A 2015 4 Pages PDF
Abstract

•We use the general set of PDEs that are satisfied by all shape-invariant potentials to find a new potential.•We report a new shape-invariant potential, which is an extension of the Morse potential.•The new potential is isospectral with Morse, but has different asymptotic values and contains free parameters.•It is a isospectral deformation of Morse, which retains the shape invariance.

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.

Related Topics
Physical Sciences and Engineering Physics and Astronomy Physics and Astronomy (General)
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