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arXiv:1006.1250 · Open Physics

Approximate analytical solutions of the effective mass Dirac equation for the generalized Hulthén potential with any κ-value

Altuğ Arda, R. Sever, C. Tezcan

Published Dec 7, 2009• 7 citations
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Abstract

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.

DOI
10.2478/s11534-009-0163-0

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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.
Approximate κ\kappaκ -state solutions of the Dirac equation in spatially dependent mass for the Eckart potential including the Yukawa tensor interaction
We investigate the analytical approximation to arbitrary -state solutions of the Dirac equation with the position-dependent mass particle in the Eckart potential including the Yukawa tensor interaction in the framework of a parametric Nikiforov–Uvarov method. By taking a proper approximation to deal with the centrifugal term, the analytical relativistic energy eigenvalues and the corresponding normalized two-spinor components of the wave function are obtained in closed form. The relativistic and non-relativistic bound state solutions for some special cases, such as the Hulthén potential and the generalized Morse potential, are easily obtained from our general solution.
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