  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.
