Solutions of the spatially-dependent mass Dirac equation with the spin and pseudospin symmetry for the Coulomb-like potential

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IKHDAİR S., Sever R.

APPLIED MATHEMATICS AND COMPUTATION, vol.216, no.2, pp.545-555, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 216 Issue: 2
  • Publication Date: 2010
  • Doi Number: 10.1016/j.amc.2010.01.072
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.545-555
  • Keywords: Dirac equation, Spin symmetry, Pseudospin symmetry, Bound states, Coulomb potential, Spatially-dependent mass, Nikiforov-Uvarov method, DIMENSIONAL SCHRODINGER-EQUATION, EXACT QUANTIZATION RULE, KLEIN-GORDON EQUATIONS, RELATIVISTIC SOLUTION, EQUAL SCALAR, APPROXIMATION, PARTICLE, STATES
  • Middle East Technical University Affiliated: Yes

Abstract

We study the effect of spatially-dependent mass function over the solution of the Dirac equation with the Coulomb potential in the (3 + 1)-dimensions for any arbitrary spin-orbit kappa state. In the framework of the spin and pseudospin symmetry concept, the analytic bound state energy eigenvalues and the corresponding upper and lower two-component spinors of the two Dirac particles are obtained by means of the Nikiforov-Uvarov method, in closed form. This physical choice of the mass function leads to an exact analytical solution for the pseudospin part of the Dirac equation. The special cases kappa = +/- 1(l = (l) over bar = 0; i.e., s-wave), the constant mass and the non-relativistic limits are briefly investigated. (C) 2010 Elsevier Inc. All rights reserved.