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

Authors Abdelmadjid Maireche

Laboratory of Physics and Material Chemistry, Physics Department, Sciences Faculty, University of M'sila-M’sila Algeria

Е-mail abmaireche@gmail.com
Issue Volume 10, Year 2018, Number 6
Dates Received 08 July 2018; revised manuscript received 28 November 2018; published online 18 December 2018
Citation Abdelmadjid Maireche, J. Nano- Electron. Phys. 10 No 6, 06015 (2015)
DOI https://doi.org/10.21272/jnep.10(6).06015
PACS Number(s) 11.10.Nx, 32.30 – r, 03.65 – w
Keywords Schrödinger equation (5) , Coulomb potentials plus linear and harmonic radial terms, Noncommutative space-phase (3) , Star product and Generalized Bopp’s shift method (2) .

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.

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