Simple unified derivation and solution of Coulomb, Eckart and Rosen-Morse potentials in prepotential approach

TL;DR

This paper presents a unified method using the prepotential approach to derive and solve Coulomb, Eckart, and Rosen-Morse potentials, simplifying their treatment and highlighting their similarities.

Contribution

It extends the prepotential approach to unify the derivation and solution of these related exactly solvable models.

Findings

Unified derivation of Coulomb, Eckart, Rosen-Morse potentials

Simplified solution process for these models

Highlights the common structure of these potentials

Abstract

The four exactly-solvable models related to non-sinusoidal coordinates, namely, the Coulomb, Eckart, Rosen-Morse type I and II models are normally being treated separately, despite the similarity of the functional forms of the potentials, their eigenvalues and eigenfunctions. Based on an extension of the prepotential approach to exactly and quasi-exactly solvable models proposed previously, we show how these models can be derived and solved in a simple and unified way.