Noncommutative Dirac and Schrödinger equations in the background of the new generalized Morse potential and a class of Yukawa potential with the improved Coulomb-like tensor potential as a tensor in 3D-ERQM and 3D-ENRQM symmetries.

Relativistic and nonrelativistic quantum mechanics formulated in a noncommutative space–space have recently become the object of renewed interest. In the context of three-dimensional extended relativistic quantum mechanics (3D-ERQM) symmetries with arbitrary spin-orbit coupling quantum number k , we approximate to solve the deformed Dirac equation for a new suggested new generalized Morse potential and a class of Yukawa potential including improved Coulomb-like tensor interaction (N(GMP-CYP) plus ICLTI). 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 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 nonlinear and exponential 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 e , r e , a , b , c), the range of the potential α and noncommutativity parameters (Θ , τ , χ). We have studied the nonrelativistic limit of new spin symmetry under the N(GMP-ICYP) model, we will also treat some important special cases such as the new generalized Morse potential, the new class of Yukawa potential, the new Hellmann potential, the new inversely quadratic Yukawa potential, the new Hulthén potential and new Coulomb potential. Finally, we studied a case of composite systems. [ABSTRACT FROM AUTHOR]