Approximate arbitrary (k,l) states solutions of deformed Dirac and Schrödinger equations with new generalized Schiöberg and Manning–Rosen potentials within the generalized tensor interactionsin 3D-EQM symmetries.

Relativistic and nonrelativistic quantum mechanics formulated in a noncommutative space-space have recently become the object of renewed interest. In the context of extended relativistic quantum mechanics (ERQM) symmetries with arbitrary spin-orbit coupling quantum number k , we approximate to solve the deformed Dirac equation (DDE) for a new suggested new generalized Schiöberg and Manning–Rosen potentials within the generalized (Coulomb and Yukawa)-like tensor interactions (NGSM-GLTs). In 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 quantum mechanics (RQM) as the main part plus three corrected parts produced from the effect of the spin-orbit interaction, the new modified Zeeman, and the rotational Fermi term, by using the parametric of the well-known Bopp's shift method and standard perturbation theory using Greene–Aldrich approximation to handle 1 / r , 1 / r 2 and other terms in the effective potential. The new values that we got appeared sensitive to the quantum numbers (j , k , l / l ̃ , s / s ̃ , m / m ̃), the mixed potential depths ( D 0 , D 1 , σ , α , A), the range of the potential δ , and noncommutativity parameters (Θ , τ , χ). We recovered several potentials, including the improved Schiöberg and Manning–Rosen potentials within the improved Yukawa-like tensor interaction, the new Schiöberg and Manning–Rosen potentials within the improved Coulomb-like tensor interaction, the new Schiöberg potential within the improved Yukawa-like tensor interaction, the new Manning–Rosen potential within the improved Yukawa-like tensor interaction, and the new Schiöberg and Manning–Rosen potentials potential problems in the context of nonrelativistic extended quantum mechanics symmetries. [ABSTRACT FROM AUTHOR]