Solvable rational extension of translationally shape invariant potentials

摘要

Combining recent results on rational solutions of the Riccati-Schr?dinger equations for shape invariant potentials to the scheme developed by Tkachuk, 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 second category.