New Approximate Solutions to a Spatially-Dependent Mass Dirac Equation for Modified Hylleraas Plus Eckart Potential with Improved Yukawa Potential as a Tensor in the DQM Framework

In this work, the bound state solutions of the deformed Dirac equation (DDE) have been investigated with the improved spatially-dependent mass modified Hylleraas plus Eckart potential including a Yukawa-like tensor interaction (IMHEP-YLT) model under the condition of spin (p-spin) symmetry in the context of extended relativistic quantum mechanics ERQM symmetries. The spatially-dependent mass modified Hylleraas plus Eckart potential including a Yukawa-like tensor interaction (MHEP-YLT) is extended to include new central potentials (s2(1-s)4, s3/2(1-s)2, s3/2(1-s)3, s5/2(1-s)3,s5/2(1-s)4, s2(1-s)3, s(1-s)3and s3(1-s)4) which coupled with couplings (LΘ and L~ Θ) that traduced the interaction between physical properties of the system and the topological deformations of space-space, to become IMHEP-YLT model. In the framework of the parametric Bopp’s shift method and standard perturbation theory, the new relativistic and non-relativistic energy eigenvalues for the IMHEP-YLT have been obtained. The new values that we got appeared sensitive to the quantum numbers (j, k, l, l~ , s, s~ , m, m~), the mixed potential depths (a, b, V, V, V, m, U), and noncommutativity parameters (Θ ,τ,χ). We have addressed some important special cases within the framework of relativistic extended quantum mechanics that we believe are useful to the specialist researcher. We have also, treated the non-relativistic limits of obtained energy under spin symmetry under the transformations known in the literature that we applied in the framework of ERQM symmetries. We recovered the usual results of relativistic and non-relativistic in the literature when we apply the three simultaneous limits (Θ , τ, χ) → (0 , 0 , 0) for the physical systems which interacted with the MHEP-YLT model.