Nonrelativistic Bound State Solutions of the Modified 2D-Killingbeck Potential Involving 2D-Killingbeck Potential and Some Central Terms for Hydrogenic Atoms and Quarkonium System

Authors Abdelmadjid Maireche

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

Issue Volume 11, Year 2019, Number 4
Dates Received 20 December 2018; revised manuscript received 02 August 2019; published online 22 August 2019
Citation Abdelmadjid Maireche, J. Nano- Electron. Phys. 11 No 4, 04024 (2019)
PACS Number(s) 11.10.Nx, 32.30 – r, 03.65 – w
Keywords Schrödinger equation (5) , Killingbeck potential, Noncommutative space–phase, Star product and generalized Bopp’s shift method (2) .

In the paper, a new nonrelativistic analytical model is presented and used to modify the Schrödinger equation for atomic scales with two dimensional modified Killingbeck potential (2DMKBP) for the hydrogenic atoms and quarkonium system in noncommutative two-dimensional real space-phase (NC: 2D-RSP). We applied the generalized Bopp’s shift method to obtain 2DMKBP involving ordinary 2D-Killingbeck potential (2DKBP) and some central terms proportional to the two infinitesimals parameters EMBED Equation.DSMT4 . We have also observed the new kinetic term composed of ordinary kinetic term and additive part proportional to infinitesimals parameter EMBED Equation.DSMT4 . Furthermore, the global Hamiltonian operator for 2DMKBP involves three fundamental parts: the first one is the ordinary Hamiltonian operator in commutative quantum mechanics (CQM), the second part is the spin-orbit operator EMBED Equation.DSMT4 , while the third is the modified Zeeman operator EMBED Equation.DSMT4 . Thus, the global energy will include in addition to the ordinary energy in CQM two principal corrections ( EMBED Equation.DSMT4 , EMBED Equation.DSMT4 ) and  EMBED Equation.DSMT4  corresponding to the spin-orbit interaction and modified Zeeman effect, respectively. The global energy levels  EMBED Equation.DSMT4  depend on discrete atomic quantum numbers  EMBED Equation.DSMT4  and the parameters of studied potential EMBED Equation.DSMT4 . Moreover, we have generalized the obtained results to include the quarkonium system ( EMBED Equation.DSMT4  and EMBED Equation.DSMT4 ). We have also shown that the mass spectra of quarkonium system were changed to the new forms. The previous results in CQM become special cases when we make the simultaneously two limits EMBED Equation.DSMT4 .