Bulg. J. Phys. vol.49 no.3 (2022), pp. 239-265

Analytical Expressions to Energy Eigenvalues of the Hydrogenic Atoms and the Heavy Light Mesons in the Framework of 3D-NCPS Symmetries Using the Generalized Bopp's Shift Method

Abdelmadjid Maireche
Laboratory of Physics and Material Chemistry, Physics Department, Sciences Faculty, University of M'sila, P.O.B. 239, CHEBILIA M'sila, Algeria
Abstract. In the present paper, within the framework of the Deformed Schrödinger equation, using the generalized Bopp's shift method and standard perturbation theory, we have obtained the energy eigenvalues of a newly proposed improved trigonometric Rosen-Morse potential model (ITRMP) for the hydrogenic atoms and the Heavy Light Mesons (HLM) QǬ (Q = b,c) and we also applied the results obtained in the production of the modified mass-spectra of the HLM in the three-dimensional nonrelativistic noncommutative phase space (3D-NCPS) symmetries. The potential is a superposition of the trigonometric Rosen-Morse potential and new central terms appear as a result of the effects of noncommutativity properties of space and phase on the TRMP model. The obtained energy eigenvalues and modified mass spectra appeared as a function of the discreet atomic quantum numbers (j, n, l, s and m), infinitesimal parameters (Θ, λ and τ) and (η, ¯λ and ¯τ) which are induced by (space-space) and (phase-phase), in addition to, the dimensional parameters (μ, b, d) of the studied potential. Furthermore, we have shown that the corresponding new Hamiltonian operator is the sum of the ordinary Hamiltonian operator of the TRMP model and three operators, the first one is the modified spin-orbit interaction, the second is the modified Zeeman operator while the third part is the rotational part for the previous hydrogenic and the HLM systems.

doi: https://doi.org/10.55318/bgjp.2022.49.3.239

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