The influence of noncommutativity on the energy spectra of bosonic particles in the framework of the DKGE with improved spatially-dependent mass including mixed scalar-vector Coulomb potentials in the ERQM symmetries

The bound state solutions of the deformed Klien-Gordon equation (DKGE) have been determined in the extended relativistic quantum mechanics ERQM symmetries using the improved spatially-dependent mass Coulomb potential with mixed scalar-vector Coulomb potentials (ISDM-SVCPs) model. The spatially-dependent mass Coulomb potential, as well as a combination of ((1/(r³)) and (1/(r⁴))), are included in the ISDM-SVCPs model, which is coupled with the coupling LΘ, which explains the interaction of the physical features of the system with the topological deformations of space-time. The new relativistic energy eigenvalues for the ISDM-CP have been derived using the parametric Bopp's shift method and standard perturbation theory. Quantum numbers (j,l,s,m), mixed potential depths (q/s_{c},m₀,m₁), and noncommutativity parameters (Θ,τ,χ) seemed to affect the new values we obtained. Within the framework of relativistic extended quantum mechanics, we have addressed certain significant particular instances that we hope will be valuable to the specialized researcher. In DKGE symmetries, we've also looked at the improved pure scalar Coulomb-like potential. The formulation of total energy was also discovered in the context of extended symmetries, which unified the energies of bosonic particles and antiparticles into a single mathematical formula. When the three simultaneous limits (Θ,τ,χ) were applied, we recovered the normal results of relativistic in the literature (0,0,0).