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

Abstract

The properties of the modified Pöschl-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.

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