Generation of a novel exactly solvable potential

作者：Bougie Jonathan; Gangopadhyaya Asim^*; Mallow Jeffry V; Rasinariu Constantin

来源：Physics Letters, Section A: General, Atomic and Solid State Physics , 2015, 379(37): 2180-2183.

DOI：10.1016/j.physleta.2015.06.058

• Supersymmetric quantum mechanics
• Shape invariance
• Exactly solvable systems.
• Extended potentials
• Isospectral deformation

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

• 出版日期2015-10-2