Approximate k-state solutions of the deformed Dirac equation in spatially dependent mass for the improved Eckart potential including the improved Yukawa tensor interaction in ERQM symmetries

In this work. we considered analytical approximate bound state solutions of the mass-dependent deformed Dirac equation with the improved vector Eckart potential including the Yukawa tensor interaction (IEPDMYI for short) in the context of extended relativistic quantum mechanics ERQM symmetries. The new relativistic energy spectra of the DDE for the IEPDMYI with spin symmetry and pseudospin symmetry are obtained. The solutions for arbitrary k-wave are obtained by using the basic concept of Bopp's shift approach and standard perturbation by applying an approximation to the centrifugal-like term in the calculations. The new values that we get appeared sensitive to the discrete quantum numbers (j, k, l, (l) over tilde, s, (s) over tilde, m, (m) over tilde), the mixed potential depths (V-1, V-2, V-0), the range of the potential ce and noncommutativity parameters (Theta, sigma, chi). We have highlighted three physical phenomena that automatically generate a result of the topological properties of noncommutativity, the first physical phenomena are the perturbative spin-orbit coupling, the second is the magnetic induction while the third corresponds to the rotational proper phenomena. We show that the corrections on the spectrum energy are smaller than the main energy in the usual cases of quantum field theory. In the ERQM symmetries, it is not possible to get the exact analytical solutions for (k = 0, -1, +1), only the approximate solutions are available. We have obtained the energy equation for several well-known potentials by choosing appropriate parameters in the improved Eckart potential model such as the improved Hulthen potential and the improved generalized Morse potential.