Realization of the spectrum generating algebra for the generalized Kratzer potentials

TL;DR

This paper explores the dynamical symmetries of generalized Kratzer molecular potentials using the factorization method, establishing ladder operators and calculating matrix elements and energy eigenvalues for diatomic molecules.

Contribution

It introduces a simple factorization approach to derive the spectrum generating algebra and matrix elements for generalized Kratzer potentials, providing results consistent with existing methods.

Findings

Exact bound state energies for CO and NO molecules are computed.

Matrix elements of relevant operators are obtained in closed form.

Results agree well with previous calculations.

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.