Rational solutions for the Riccati-Schrödinger equations associated to translationally shape invariant potentials

Yves Grandati (1) , Alain Bérard (1)

1 FCN - Fédération de Chimie de Nancy

We develop a new approach to build the eigenfunctions of a translationally shape-invariant potential. For this we show that their logarithmic derivatives can be expressed as terminating continued fractions in an appropriate variable. We give explicit formulas for all the eigenstates, their specific form depending on the Barclay-Maxwell class to which the considered potential belongs.

Mots clés: supersymmetric quantum mechanics; shape invariant potentials; solvable models; Riccati equation

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]; Physique Quantique [quant-ph]

Yves Grandati, Alain Bérard. Rational solutions for the Riccati-Schrödinger equations associated to translationally shape invariant potentials. Annals of Physics, 2010, 325, pp.1235-1259. ⟨10.1016/j.aop.2010.03.008⟩. ⟨hal-00426370v3⟩