Revisiting an isospectral extension of the Morse potential

TL;DR

This paper introduces a straightforward method to create isospectral extensions of the Morse potential and uses transformations to connect these to quasi-exactly solvable extensions of other important potentials.

Contribution

The paper presents a simple technique for deriving isospectral Morse potential extensions and links them to solvable extensions of radial oscillator and Coulomb potentials via point canonical transformations.

Findings

Derived a simple method for isospectral Morse potential extensions

Connected Morse extensions to quasi-exactly solvable radial and Coulomb potentials

Demonstrated transformations between different quantum potentials

Abstract

A very simple method is devised to derive a (strictly) isospectral extension of the Morse potential. Furthermore, point canonical transformations are used to transform the latter into quasi-exactly solvable extensions of the radial oscillator and the Coulomb potentials.