Solvable rational extensions of the isotonic oscillator

Yves Grandati (1)

1 FCN - Fédération de Chimie de Nancy

Combining recent results on rational solutions of the Riccati-Schrödinger equations for shape invariant potentials to the finite difference Bäcklund algorithm and specific symmetries of the isotonic potential, we show that it is possible to generate the three infinite sets (L1, L2 and L3 families) of regular rational solvable extensions of this potential in a very direct and transparent way.

Mots clés: exactly solvable systems; SUSY quantum mechanics; Darboux-Bäcklund transformations; shape invariance

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

Yves Grandati. Solvable rational extensions of the isotonic oscillator. 2010. ⟨hal-00549822v2⟩