Prepotential approach to solvable rational extensions of Harmonic Oscillator and Morse potentials

TL;DR

This paper introduces a direct, systematic method to construct solvable rational extensions of the Harmonic Oscillator and Morse potentials, bypassing traditional techniques like supersymmetry and Darboux transformations.

Contribution

It presents a novel approach for deriving rational extensions of these potentials without relying on supersymmetry or shape invariance.

Findings

Constructed new rational extensions systematically

Eliminated need for supersymmetry and Darboux transformations

Provided explicit solutions for extended potentials

Abstract

We show how the recently discovered solvable rational extensions of Harmonic Oscillator and Morse potentials can be constructed in a direct and systematic way, without the need of supersymmetry, shape invariance, Darboux-Crum and Darboux-B\"acklund transformations