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23. THE D-DIMENSIONAL SCHRÖDINGER EQUATION FOR MULTIPARAMETER-TYPE POTENTIAL (MPP) AND ITS THERMODYNAMIC PROPERTIES USING NIKIFOROV-UVAROV (NU) METHOD by Hillary P. Obong and Uduakobong S. Okorie
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THE D-DIMENSIONAL SCHRÖDINGER EQUATION FOR MULTIPARAMETER-TYPE POTENTIAL (MPP) AND ITS THERMODYNAMIC PROPERTIES USING NIKIFOROV-UVAROV (NU) METHOD

Hillary P. Obong1 and Uduakobong S. Okorie1,2

1. Department of Physics, Theoretical Physics Group, University of Port Harcourt, Choba, Nigeria.

2. Department of Physics, AkwaIbom State University, IkotAkpaden, P.M.B. 1167, Uyo, Nigeria.

Abstract

In our study, the Pekeris approximation scheme and Nikiforov-Uvarov (NU) method are applied to obtain the energy eigenvalues of the d-dimensional Schrӧdinger equation with a multiparameter-type potential (MPP). The normalized energy eigenfunctions were also obtained in terms of the hypergeometric polynomials. Numerical results of the energy eigenvalues were obtained in different dimensions, and they agree with results in the literature. With appropriate values for the potential parameters, the effects of the potential parameters on the energy eigenvalues were evaluated graphically. The eigenvalues of the energy relation for the MPP were employed to evaluate the vibrational partition function and other thermodynamic properties for certain temperatures and upper bound vibrational quantum numbers. Finally, variations of the thermodynamic properties with certain temperatures and upper bound vibrational quantum numbers were analyzed and discussed extensively. 

Keywords: Multiparameter potential, Schrӧdinger equation, Nikiforov-Uvarov method, Vibrational Partition function.PACS Nos.: 03.65.Ge, 03.65.Pm, 03.65.Ca. 

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