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arXiv:1005.3117 · Chinese Physics Letters

Effective Mass Dirac–Morse Problem with any κ -value

Altuğ Arda, R. Sever, C. Tezcan, Hüseyin Akçay

Published Apr 1, 2010• 9 citations
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Abstract

The Dirac–Morse problem is investigated within the framework of an approximation to the term proportional to 1/ r 2 in the view of the position-dependent mass formalism. The energy eigenvalues and corresponding wave functions are obtained by using the parametric generalization of the Nikiforov–Uvarov method for any κ -value. We also study the approximate energy eigenvalues, and the corresponding wave functions in the case of the constant-mass for pseudospin, and spin cases, respectively.

DOI
10.1088/0256-307x/27/4/040306

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The Dirac–Morse problem is investigated within the framework of an approximation to the term proportional to 1/ r 2 in the view of the position-dependent mass formalism. The energy eigenvalues and corresponding wave functions are obtained by using the parametric generalization of the Nikiforov–Uvarov method for any κ -value. We also study the approximate energy eigenvalues, and the corresponding wave functions in the case of the constant-mass for pseudospin, and spin cases, respectively.
Abstract The Dirac equation, with position-dependent mass, is solved approximately for the generalized Hulthén potential with any spin-orbit quantum number κ. Solutions are obtained by using an appropriate coordinate transformation, reducing the effective mass Dirac equation to a Schrödinger-like differential equation. The Nikiforov-Uvarov method is used in the calculations to obtain energy eigenvalues and the corresponding wave functions. Numerical results are compared with those given in the literature. Analytical results are also obtained for the case of constant mass and the results are in good agreement with the literature.
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
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.