A New Relativistic Study for Interactions in One-electron atoms (Spin ½ Particles) with Modified Mie-type Potential

Abstract

In this paper, we present a novel theoretical analytical perform further investigation for the exact solvability of relativistic quantum spectrum systems for modified Mie-type potential (m.m.t.) potential is discussed for spin-1/2 particles by means Boopp’s shift method instead to solving deformed Dirac equation with star product, in the framework of noncommutativity three dimensional real space (NC: 3D-RS). The exact corrections for excited n th states are found straightforwardly for interactions in one-electron atoms by means of the standard perturbation theory. Furthermore, the obtained corrections of energies are depended on four infinitesimal parameter Θ ,which induced by position-position noncommutativity, in addition to the discreet atomic quantum numbers: j l s l ± 1/ 2,s = ± 1/ 2, and m (the angular momentum quantum number) and we have also shown that, the usual states in ordinary two and three dimensional spaces are canceled and has been replaced by new degenerated 2 ( 2 1 + 1 ) sub-states in the new uantum symmetries of (NC: 3D-RS) and we have also applied our obtained results to the case of modified KrazerFutes potential.