A new dynamical group approach to the modified Poschl-Teller potential

TL;DR

This paper introduces a novel dynamical group method for the modified Pöschl-Teller potential, constructing ladder operators directly from wave functions and linking the $su(2)$ algebra to molecular vibrational models.

Contribution

It presents a new approach to analyze the MPT potential using $su(2)$ algebra, deriving explicit operators and connecting quantum vibrational models.

Findings

Ladder operators are constructed directly from wave functions.

Operators are associated with the $su(2)$ algebra.

Establishes an exact connection between $su(2)$ vibron model and molecular vibrations.

Abstract

The properties of the modified P\"{o}schl-Teller (MPT) potential are outlined. The ladder operators are constructed directly from the wave functions without introducing any auxiliary variable. It is shown that these operators are associated to the $su(2)$ algebra. Analytical expressions for the functions $\sinh(\alpha x)$ and $\frac{\cosh(\alpha x)}{\alpha} \frac{d}{dx}$ are evaluated from these ladder operators. The expansions of the coordinate $x$ and momentum $\hat p$ in terms of the $su(2)$ generators are presented. This analysis allows to establish an exact quantum-mechanical connection between the $su(2)$ vibron model and the traditional descriptions of molecular vibron.