Mapping of shape invariant potentials by the point canonical transformation

TL;DR

This paper uses point canonical transformations to relate various shape invariant potentials in quantum mechanics, revealing their algebraic structures and classifications.

Contribution

It demonstrates mappings between Coulomb, Kratzer, and Morse potentials, and classifies their algebraic structures, expanding understanding of shape invariant potentials.

Findings

Coulomb and Kratzer potentials map to Morse potential

Pöschl-Teller type I shares algebraic structure with Hulthén

Different shape invariant potentials have distinct algebraic groups

Abstract

In this paper by using the method of point canonical transformation we find that the Coulomb and Kratzer potentials can be mapped to the Morse potential. Then we show that the P\"{o}schl-Teller potential type I belongs to the same subclass of shape invariant potentials as Hulth\'{e}n potential. Also we show that the shape-invariant algebra for Coulomb, Kratzer, and Morse potentials is SU(1,1), while the shape-invariant algebra for P\"{o}schl-Teller type I and Hulth\'{e}n is SU(2).