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

• Published in: Applied mathematics and computation 2010-03, Vol.216 (2), p.545-555
• Main Authors: Ikhdair, Sameer M., Sever, Ramazan
• Format: Article
• Language: English
• Subjects: Algebra; Bound states; Coulomb potential; Dirac equation; Eigenvalues; Energy of formation; Exact sciences and technology; Exact solutions; Linear and multilinear algebra, matrix theory; Mathematical analysis; Mathematical models; Mathematics; Nikiforov–Uvarov method; Nonlinear algebraic and transcendental equations; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Pseudospin symmetry; Sciences and techniques of general use; Spatially-dependent mass; Spin symmetry; Symmetry
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2010.01.072

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 κ 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 κ = ± 1 ( l = l ˜ = 0 ,i.e . , s -wave ) , the constant mass and the non-relativistic limits are briefly investigated.