A Nonrelativistic Subatomic Model to Describe a Behavior of 2D Anharmonic Sextic Potential for Atomic Nucleus in the Symmetries of Extended 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 11, Year 2019, Number 1
Dates Received 12 September 2018; revised manuscript received 01 February 2019; published online 25 February 2019
Citation Abdelmadjid Maireche, J. Nano- Electron. Phys. 11 No 1, 01024 (2019)
DOI https://doi.org/10.21272/jnep.11(1).01024
PACS Number(s) 11.10.Nx, 32.30 – r, 03.65 – w, 03.65.Ca, 03.65.Ge
Keywords Schrödinger equation (5) , Anharmonic sextic potential, Noncommutative space-phase (3) , Star product and generalized Bopp’s shift method (2) .

In the present work, a nonrelativistic analytical model is presented and used to modify the Schrödinger equation for subatomic scales with two-dimensional new anharmonic sextic potential (2DNASP) for atomic nuclei in noncommutative two-dimensional real space-phase (NC: 2D-RSP). We applied the generalized Bopp’s shift method to obtain 2DNASP, which is composed of ordinary anharmonic sextic potential and new additive part proportional to the infinitesimal parameter ?. We have also observed the kinetic term containing a new additive part proportional to the infinitesimal parameter . Thus, the global potential proportional to two infinitesimal parameters allowed us to consider the perturbation terms due to (space-phase) noncommutativity. Furthermore, the standard perturbation theory allowed us to find the corrections  and  corresponding to spin-orbital interaction and modified Zeeman effect, respectively. These corrections allowed us to find global energy levels , which depend on the discrete atomic quantum numbers (jlsm) and the parameters of the studied potential (abc), and we constricted the corresponding Hamiltonian operator . We have also generalized our obtained results to include the other nuclei’s atoms with spin  differs from . This study has allowed us to obtain the energy spectrum in the extended quantum mechanics, which interpreted three physical phenomena. The first one is an ordinary two-dimensional new anharmonic sextic potential, while the second and third are the automatic appearance of spin-orbit interaction and modified magnetic influence, these phenomena were generated from the property of noncommutativity of space and phase. The obtained analytical results (the energy eigenvalues and the corresponding Hamiltonian operator) are in good agreement with the existing results. The previous results, in ordinary quantum mechanics, become special cases when we make simultaneously the limits .

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