Realization of the spectrum generating algebra for the generalized Kratzer potentials

Abstract

The dynamical symmetries of the Kratzer-type molecular potentials (generalized Kratzer molecular potentials) are studied by using the factorization method. The creation and annihilation (ladder) operators for the radial eigenfunctions satisfying quantum dynamical algebra $SU(1, 1)$ are established. Factorization method is a very simple method of calculating the matrix elements from these ladder operators. The matrix elements of different functions of $r$, $r\frac{d}{dr}$, their sum $\Gamma_{1}$ and difference $\Gamma_{2}$ are evaluated in a closed form. The exact bound state energy eigenvalues $E_{n, \ell}$ and matrix elements of $r$, $r\frac{d}{dr}$, their sum $\Gamma_{1}$ and difference $\Gamma_{2}$ are calculated for various values of $n$ and $\ell$ quantum numbers for $CO$ and $NO$ diatomic molecules for the two potentials. The results obtained are in very good agreement with those obtained by other methods.