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.

20pages, 1 figure

References in corpus (2)

• Exact solutions of the radial Schrodinger equation for some physical potentials
• On the solutions of the Schrodinger equation with some molecular potentials: wave function ansatz

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• Closed analytical solutions of the d-dimensional Schrödinger equation with deformed Woods-Saxon potential plus double ring-shaped potential
• Lie algebraic solution of the Kratzer oscillator in diatomic molecules
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