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Communications in Theoretical Physics

Bound State Solutions of Schrödinger Equation for Generalized Morse Potential with Position-Dependent Mass

Altuğ Arda, R. Sever

Published Jul 1, 2011• 22 citations
Publisher

Abstract

The effective mass one-dimensional Schrödinger equation for the generalized Morse potential is solved by using Nikiforov—Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.

DOI
10.1088/0253-6102/56/1/09

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The effective mass one-dimensional Schrödinger equation for the generalized Morse potential is solved by using Nikiforov—Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.
We solve the parametric generalized effective Schrödinger equation with a specific choice of position-dependent mass function and Morse oscillator potential by means of the Nikiforov–Uvarov method combined with the Pekeris approximation scheme. All bound-state energies are found explicitly and all corresponding radial wave functions are built analytically. We choose the Weyl or Li and Kuhn ordering for the ambiguity parameters in our numerical work to calculate the energy spectrum for a few (H2, LiH, HCl and CO) diatomic molecules with arbitrary vibration n and rotation l quantum numbers and different position-dependent mass functions. Two special cases including the constant mass and the vibration s-wave (l = 0) are also investigated.
Effective mass Schrödinger equation is solved exactly for a given potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function. The effective mass Schrödinger equation is also solved for the Morse potential transforming to the constant mass Schrödinger equation for a potential. One can also get solution of the effective mass Schrödinger equation starting from the constant mass Schrödinger equation. PACS numbers: 03.65.-w; 03.65.Ge; 12.39.Fd Keywords: Position-dependent mass, Effective mass Schrödinger equation, Morse potential, Nikiforov-Uvarov method