New relativistic and non-relativistic investigation of deformed Klein-Gordon and Schrodinger equations for new improved screened Kratzer potential in the framework of non-commutative space

The deformed Klein-Gordon equation has been solved in three-dimensional extended relativistic quantum mechanics (3D-ERQM) symmetries for the newly improved screened Kratzer potential (NISKP) model under the influence of the deformation space-space symmetries. The new relativistic energy eigenvalues were calculated using the parametric Bopp ' s shift method and standard perturbation theory in addition to the approximation scheme suggested by Greene and Aldrich for the inverse square terms. The new relativistic energy eigenvalues of (LiH, HCl, CO and H-2) molecules under the NISKP model were shown to be sensitive to the atomic quantum numbers ( j, l, s, m), mixed potential depths (D-e, r(e)), the screening parameter ' s inverse (alpha, beta), control parameter t and non-commutativity parameters (Theta, ss,zeta). In addition, we analyzed the non-relativistic energy values by applying the well-known transmission rules known in the literature. Furthermore, we studied many special cases useful to researchers in the framework of the new extended symmetries, such as the new screened cosine Kratzer potential, the new screened Kratzer potential (SKP), the new Kratzer potential, the new coshine Yukawa potential, the new coshine Yukawa potential, the new shifted improved SKP and the new shifted SKP. The study is further extended to calculate the mass spectra of mesons of the heavy quarkonium system such as charmonium cc, bottomonium bb, bc and light mesons cs and bs that have the quark and antiquark flavor within the framework of the NISKP model in 3D-ENRQM symmetries.