Extended of the Schrödinger Equation with New Coulomb Potentials plus Linear and Harmonic Radial Terms in the Symmetries of Noncommutative Quantum Mechanics

Abstract

In this recently work, we have obtained the analytical solutions of the modified Schrödinger equation (MSE) with new Coulomb potentials plus linear and harmonic radial terms (NCPLHRT) for hydrogenic atoms in noncommutative 3-dimensional real space-phase (NC: 3D-RSP). We applied, the generalized Bopp’s shift method and standard perturbation theory in the framework of two infinitesimal parameters due to (space-phase) noncommutativity, we obtained new energy eigenvalues, which depended with discrete atomic quantum numbers and parameters of studied potential, in addition to the corresponding new Hamiltonian operator. Our research also conveys another innovative feature, the global group symmetry (NC: 3D-RSP) were broken simultaneously and replaced by the residual local subgroup (NC: 3D-RS) under interaction of hydrogenic atoms with NCPLHRT.