Generalized Morse and Poschl-Teller potentials : The connection via Schrodinger equation

TL;DR

This paper unifies the treatment of generalized Morse and Poschl-Teller potentials in the Schrödinger equation, revealing their connection through Fourier and Hankel transforms, and providing a systematic framework for their analysis.

Contribution

It introduces a unified approach linking Morse and Poschl-Teller potentials via integral transforms, enhancing understanding of their mathematical relationship.

Findings

Wave functions are connected through Fourier transforms.

Generalized potentials are linked via Hankel transforms.

The approach provides a systematic framework for potential analysis.

Abstract

We present here a systematic and unified treatment to connect the Schrodinger equation corresponding to generalized Morse and Poschl-Teller potentials. We then show that the wave functions and generalized potentials are linked through the Fourier and Hankel transforms, respectively.