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 th n 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  ,which induced by position-position noncommutativity, in addition to the discreet atomic quantum numbers: 1 / 2, 1 / 2, j l s l     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number) and we have also shown that, the usual states in ordinary two and three dimensional spaces are canceled and has been replaced by new degenerated   2 2 1 l  sub-states in the new quantum symmetries of (NC: 3D-RS) and we have also applied our obtained results to the case of modified Krazer-Futes potential.

Effects of Two-Dimensional Noncommutative Theories on Bound States Schrödinger Diatomic Molecules under New Modified Kratzer-Type Interactions

“…In order to construct a 2D model of NMKP, the essential step is to rewrite the ordinary SE to the new following modified Schrödinger equation (MSE) which play a major role in (NC: 2D-RSP) symmetries [23][24][25][26][27][28][29][30][31][32][33][34]:…”

“…In this sub-section we apply the same strategy, which we have seen in our previously works [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] …”

Investigations on the Relativistic Interactions in One-Electron Atoms with Modified Yukawa Potential for Spin 1/2 Particles

“…The three-generalized coordinates  by the following relations, as follows [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]: …”

“…which allow us to getting the operator 2 r on NC three dimensional spaces as follows [28][29][30][31][32][33][34]: (10) the coupling 13 …”

“…Furthermore, the new equal-time anti-commutator for fermionic field operators' in NC spaces can be expressed as [28][29][30][31][32][33][34]: …”