Arbitrary (k, l) States-Solutions of the Dirac and Schrödinger Equations Interacting with Improved Spatially-Dependent Mass Coulomb Potential with an improved Coulomb-like tensor interaction Model for H-atoms from 3D-RNCS and 3D-NRNCS symmetries

Abstract

The improved spatially dependent mass Coulomb potential with an improved Coulomb-like tensor interaction (ISDM(CP-CLTI)) model has been used to investigate the new bound state solutions of the deformed Dirac equation under the condition of spin symmetry and pseudospin symmetry in the 3D-relativistic noncommutative space (3D-RNCS) symmetries. The combination of spatially dependent mass Coulomb potential with Coulomb-like tensor interaction (ISDM(CP-CLTI)) and the terms (1/r^3 and 1/r^4 ) which are connected with the induced couplings (LΘ and L ̃Θ) produced from the topological defects of space-space gives ISDM(CP-CLTI) model. The new relativistic and non-relativistic energy eigenvalues for the hydrogen atoms (H-atoms) such as He+, Li+2, and Be3+ under the ISDM(CP-CLTI) model have been derived within the parameters of the parametric Bopp shift method and standard perturbation theory. The new values E_nc^sp(n,C,m_0,m_1,H,Θ,τ,χ,j,l,s,m) and E_nc^ps(n,C,m_0,m_1,H,Θ,τ,χ,j,l,l ̃,s ̃,m ̃) that we obtained appeared to be sensitive to the quantum atomic discrete quantum numbers (j,k,l,s,m,l ̃,s ̃,m ̃), the mixed potential depths (C/q,m_0,m_1,H), and noncommutativity parameters (NP) (Θ,σ,χ). Within the context of relativistic extended quantum mechanics, we have obtained certain significant special cases that, in our view, will be interesting to the specialized researcher. When we applied the three simultaneous limitations (Θ,σ,χ)→(0,0,0), NP we were able to retrieve the typical results of relativistic and non-relativistic cases in the literature. Our new model presented new physical features compared to other models known in the literature.