A new theoretical study of the deformed unequal scalar and vector Hellmann plus modified Kratzer potentials within the deformed Klein-Gordon equation in RNCQM symmetries

In this paper, within the framework of relativistic quantum mechanics and using the improved approximation scheme to the centrifugal term for any lstates via Bopp's shift method and standard perturbation theory, we have obtained the modified energy eigenvalues of a newly proposed modified unequal vector and scalar Hellmann plus modified Kratzer potentials (DUVSHMK-Ps) for some diatomic N-2, I-2, CO, NO, O-2 and HCl molecules. This study includes corrections of the first-order in noncommutativity parameters (Theta,sigma). This potential is a superposition of the attractive Coulomb Yukawa potential plus the Kratzer potential and new central terms appear as a result of the effects of noncommutativity properties of space-space. The obtained energy eigenvalues appear as a function of noncommutativity parameters, the strength parameters (V-0,S-0) and (V-1,S-1) of the (scalar vector) Hellmann potential, the screening range parameter alpha, the dissociation energy of the vector, and scalar potential (D-v,D-s), the equilibrium inter-nuclear distance re in addition to the atomic quantum numbers (n,j,l,s,m). Furthermore, we obtained the corresponding modified energy of DUVSHMK-Ps in the symmetries of non-relativistic noncommutative quantum mechanics (NRNCQM). In both relativistic and non-relativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of RQM and NRQM.