Non-commutativity of the Klein–Gordon and Schrödinger Equations in the Background of the Improved Linear Plus Modified Yukawa Potential I(L-MYP) in 3D-(R/NR)NCQs Symmetries

This work proposes an improved linear plus modified Yukawa potential (I(L-MYP)) model in the framework of three-dimensional relativistic and non-relativistic noncommutative quantum space (3D-(R/NR)NCQs) regimes and determine its complete eigenvalue solutions based on the corresponding solutions within the framework of the symmetries of relativistic and relativistic commutative quantum mechanics (3D-(R/NR)Qm) found in the literature. The new energy spectrum in relativistic and non-relativistic regimes is obtained using the parametric Bopp shift method and standard perturbation theory. The new (R/NR) energy equation I(L-MYP) model in the presence of deformation space-space depends on atomic quantum numbers ([Formula: see text] and m), the mixed potential depths ([Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]), the inverse of the screening parameter [Formula: see text], and non-commutativity space–space parameters ([Formula: see text], [Formula: see text] and [Formula: see text]). We recovered various potentials such as the modified scalar-vector Yukawa potential, the new modified Yukawa potential and the deformed class of Yukawa potentials from I(L-MYP) model. We also obtained a new energy spectrum in 3D-(R/NR)NCQs for all the deduced potentials from I(L-MYP) model. The new non-relativistic eigenvalue solution of the I(L-MYP) model is then applied to obtain the modified masses [Formula: see text] of the heavy-light mesons ([Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]) in the quarkonium system in 3D-(NR)NCQs regimes. If we ignore all the deformations of space–space [Formula: see text], it is natural that all the physical values obtained will be identical to their corresponding values known in 3D-(NR)NCQs regimes.