Mapping of shape invariant potentials by the point canonical transformation
Mathematical Physics
2009-11-13 v1 math.MP
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).
Keywords
Cite
@article{arxiv.0805.4116,
title = {Mapping of shape invariant potentials by the point canonical transformation},
author = {M. R. Setare and E. Karimi},
journal= {arXiv preprint arXiv:0805.4116},
year = {2009}
}