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 - Abdelmadjid Maireche (Yanbu Journal of Engineering and Science, 2023)
The deformed Dirac equation has been investigated, in the context of 3D-relativistic noncommutative space (3D-RNCS) symmetries, using the improved spatially dependent mass Coulomb potential with an improved Coulomb-like tensor interaction (ISDM(CP-CLTI)) model under the conditions of spin symmetry and pseudospin symmetry. The ISDM(CP-CLTI) model is the combining the spatially dependent mass Coulomb potential with the Coulomb-like tensor interaction (CP-CLTI) and the two central terms that are generated to the topological defects of spacespace. Within the confines of the parametric Bopp shift method and conventional perturbation theory, the new relativistic and non-relativistic energy eigenvalues for the hydrogen atoms ($H$-atoms), such as $He^{+}, Li^{+2}$, and $Be^{3+}$ under the ISDM(CP-CLTI) model have been derived. The novel values $E_{n c}^{s p}\left(n, C, m_0, m_1, H, Θ, τ, χ, j, l, s, m\right)$ and $E_{n c}^{p s}\left(n, C, m_0, m_1, H, Θ, τ, χ, j, l, \tilde{l}, \tilde{s}, \tilde{m}\right)$ that we discovered examined to be dependent on the noncommutativity parameters (NP) $(Θ, σ, χ)$, mixed potential depths $\left.C / q, m_0, m_1, H\right)$, and quantum atomic discrete quantum numbers $(j, k, l, s, m, \tilde{l}, \tilde{s}, \tilde{m})$. We have obtained several interesting special examples within the framework of relativistic extended quantum mechanics, which we believe will be of interest to the expert researcher. We were able to retrieve the typical results of relativistic and non-relativistic examples in the literature when we applied the three simultaneous constraints $(Θ, σ, χ) →(0,0,0)$. Compared to previous models that are known from the literature, our new model had novel physical characteristics.