Journal of Physical Studies 26(2), Article 2001 [20 pages] (2022)
DOI: https://doi.org/10.30970/jps.26.2001

RELATIVISTIC SYMMETRIES OF THE DEFORMED DIRAC EQUATION THROUGH THE IMPROVED HULTHÉN PLUS A CLASS OF YUKAWA POTENTIAL INCLUDING A COULOMB-LIKE TENSOR INTERACTION IN DEFORMATION QUANTUM MECHANICS

Abdelmadjid Maireche 

Laboratory of Physics and Material Chemistry, Physics department,
Sciences Faculty, University of M'sila, BP 239 Chebilia-M'sila, Algeria,
e-mail: abdelmadjid.maireche@univ-msila.dz

Received 20 December 2021; in final form 24 May 2022; accepted 24 May 2022; published online 24 June 2022

We approximately solve the deformed Dirac equation for a new improved Hulthén plus a class of Yukawa potential including a Coulomb-like tensor interaction (IHCYPCTI for short) in the context of extended relativistic quantum mechanics ERQM symmetries including an improved Coulomb-like tensor interaction with an arbitrary spin-orbit coupling quantum number $k$. Within the framework of the spin and pseudospin (p-spin) symmetry, we obtain the global new energy eigenvalue which equals the energy eigenvalue in usual relativistic QM plus the corrected energy induced by three infinitesimal additive parts of the Hamiltonian corresponding to the spin-orbit interaction, the new modified Zeeman and the rotational Fermi term by using the parametric of Bopp's shift method and standard perturbation theory with an approximation to the centrifugal term. The new values that we got appeared sensitive to the quantum numbers $( j,k,l, \widetilde{l},s,\widetilde{s},m,\widetilde{m})$, the mixed potential depths $(A,B)$, the range of the potential $δ $, and noncommutativity parameters $(Θ, σ ,χ)$. The mixed potential which in some particular cases gives solutions of different potentials: the improved Hulthén, the improved Yukawa potential and the improved Coulomb-like problem along with their bound state energies are obtained.

Key words: Dirac equation, Hulthén plus a class of Yukawa potential, noncommutative geometry, Bopp's shift method and star products.

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