Application of nonlinear deformation algebra to a physical system with P\"oschl-Teller potential

TL;DR

This paper critically examines a nonlinear deformation algebra applied to the P"oschl-Teller potential, correcting previous relations and establishing accurate links with su(1,1) for better understanding of the spectrum and eigenfunctions.

Contribution

It corrects the nonlinear algebra relations for the P"oschl-Teller potential and clarifies its connection with su(1,1), providing an algebraic derivation of normalization constants.

Findings

Corrected the nonlinear algebra relation for general P"oschl-Teller potential.

Established the accurate link between the nonlinear algebra and su(1,1).

Derived the eigenfunction normalization constant algebraically.

Abstract

We comment on a recent paper by Chen, Liu, and Ge (J. Phys. A: Math. Gen. 31 (1998) 6473), wherein a nonlinear deformation of su(1,1) involving two deforming functions is realized in the exactly solvable quantum-mechanical problem with P\" oschl-Teller potential, and is used to derive the well-known su(1,1) spectrum-generating algebra of this problem. We show that one of the defining relations of the nonlinear algebra, presented by the authors, is only valid in the limiting case of an infinite square well, and we determine the correct relation in the general case. We also use it to establish the correct link with su(1,1), as well as to provide an algebraic derivation of the eigenfunction normalization constant.