Solutions of The Spatially-Dependent Mass Dirac Equation with the Spin and Pseudospin Symmetry for the Coulomb-Like Potential

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Journal Title, Volume, Page: 
Applied Mathematics and Computation, 216, 545–555
Year of Publication: 
Sameer M. Ikhdair
Department of Physics, Near East University, Nicosia, North Cyprus, Turkey
Current Affiliation: 
Department of Physics, An-Najah National University, Nablus, Palestine
Ramazan Sever
Department of Physics, Middle East Technical University, 06531 Ankara, Turkey
Preferred Abstract (Original): 

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