Solvable rational extension of translationally shape invariant potentials

TL;DR

This paper demonstrates a method to generate an infinite set of solvable rational extensions for all translationally shape invariant potentials of the second category, expanding the class of exactly solvable quantum potentials.

Contribution

It introduces a systematic approach to construct rational extensions of shape invariant potentials using Riccati-Schrödinger solutions, generalizing previous harmonic oscillator results.

Findings

Infinite solvable rational extensions constructed for each second category shape invariant potential

Extension method based on Riccati-Schrödinger equations and shape invariance principles

Potential applications in quantum mechanics for exactly solvable models

Abstract

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.