Generation of a novel exactly solvable potential

• 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.