On the interaction of an improved Schiöberg potential within the Yukawa tensor interaction under the background of deformed Dirac and Schrödinger equations

In the context of extended relativistic quantum mechanics (ERQM) symmetries with arbitrary spin–orbit coupling quantum numbers k , we approximate solve the deformed Dirac equation for a new suggested improved Schiöberg potential within Yukawa-like tensor interaction (ISPYLT). In the framework of the spin and pseudospin (p-spin) symmetry, we obtain the global new energy eigenvalue which equals the energy eigenvalue, in the 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. The new values that we got appeared sensitive to the quantum numbers j , k , l , l p , s , s p , m , m p , the mixed potential depths ( D 0 , σ , V 0 ), the range of the potential α , and noncommutativity parameters . We have also treated the nonrelativistic limit of the studied potential in NR-EQM symmetries. It is worthwhile to mention that for the simultaneous limits η , β , χ → 0 , 0 , 0 , we recover the equations of energy for the spin symmetry and the p-spin symmetry, under the Schiöberg potential, including a Yukawa-like tensor interaction which is known in the literature.