New exact bound state solutions of the deformed radial upper and lower components of Dirac equation and corresponding Hermitian anisotropic Hamiltonian operator are studied for the modified Kratzer-Fues potential (m.k.f.) potential by using Bopp’s shift method instead to solving deformed Dirac equation with star product. The corrections of energy eigenvalues are obtained by applying standard perturbation theory for interactions in one-electron atoms. Moreover, the obtained corrections of energies are depended on two infinitesimal parameters (θ, χ), which induced by position-position noncommutativity, in addition to the discreet nonrelativistic atomic quantum numbers: (j=l±1/1,s=±1/2,l and m) and we have also shown that, the usual relativistic states in ordinary three dimensional spaces are canceled and has been replaced by new degenerated 2(2l+1) sub-states in the extended quantum symmetries (NC: 3D-RS).
International Frontier Science Letters (Volume 10)
A. Maireche "A Novel Exactly Theoretical Solvable of Bound States of the Dirac-Kratzer-Fues Problem with Spin and Pseudo-Spin Symmetry", International Frontier Science Letters, Vol. 10, pp. 8-22, 2016