Solvable rational extension of translationally shape invariant potentials

Yves Grandati, Alain Berard

Published 2009-12-16, updated 2010-01-24Version 2

Combining recent results on rational solutions of the Riccati-Schr\"odinger equations for shape invariant potentials to the scheme developed by Fellows and Smith in the case of the one dimensional harmonic oscillator, we show that it is possible to generate an infinite set of solvable rational extensions for every translationally shape invariant potential of the second category.