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Realization of the Spectrum Generating Algebra for the Generalized Kratzer Potentials

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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 Γ1 and difference Γ2 are evaluated in a closed form. The exact bound state energy eigenvalues E n,ℓ and matrix elements of r, \(r\frac{d}{dr}\), their sum Γ1 and difference Γ2 are calculated for various values of n and ℓ 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.

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Authors and Affiliations

  1. Theoretical Physics Section, Department of Physics, University of Ilorin, P.M.B. 1515, Ilorin, Kwara state, Nigeria

    K. J. Oyewumi

  2. International Chair of Mathematical Physics and Applications (ICMPA-UNESCO Chair), Universite d’Abomey-Calavi, Cotonou, Republic of Benin

    K. J. Oyewumi

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  1. K. J. Oyewumi
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Correspondence to K. J. Oyewumi.

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Oyewumi, K.J. Realization of the Spectrum Generating Algebra for the Generalized Kratzer Potentials. Int J Theor Phys 49, 1302–1316 (2010). https://doi.org/10.1007/s10773-010-0311-8

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  • DOI: https://doi.org/10.1007/s10773-010-0311-8

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