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

Автор(ы) Abdelmadjid Maireche

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

Е-mail abmaireche@gmail.com
Выпуск Том 10, Год 2018, Номер 6
Даты Получено 08.07.2018; в отредактированной форме 28.11.2018; опубликовано online 18.12.2018
Ссылка 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
Ключевые слова 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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