Solvable rational extensions of the Morse and Kepler-Coulomb potentials

Yves Grandati (1)

1 FCN - Fédération de Chimie de Nancy

We show that it is possible to generate an infinite set of solvable rational extensions from every exceptional first category translationally shape invariant potential. This is made by using Darboux-Bäcklund transformations based on unphysical regular Riccati-Schrödinger functions which are obtained from specific symmetries associated to the considered family of potentials.

Mots clés: exactly solvable models; supersymmetric quantum mechanics; Darboux-Bäcklund transformations

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Physique Quantique [quant-ph]

Yves Grandati. Solvable rational extensions of the Morse and Kepler-Coulomb potentials. 2011. ⟨hal-00579161⟩