A theoretical study of the modified equal scalar and vector Manning-Rosen potential within the deformed Klein-Gordon and Schrödinger in RNCQM and NRNCQM symmetries

In this research work, within the framework of relativistic and nonrelativistic noncommutative quantum mechanics, deformed Klein–Gordon Schrödinger equations were solved with modified equal vector scalar Manning-Rosen potential that has been significance interest in recent years using Bopp's shift method standard perturbation theory first-order noncommutativity parameters 3-dimensions mechanics. By employing improved approximation centrifugal term, bound state energies obtained for some diatomic molecules such as (HCl, CH, LiH, CO, NO, O2, I2, N2, H2, Ar2). The energy eigenvalues appear a function generalized Gamma function, noncommutativity, studied potential, addition to atomic numbers . both problems, we show corrections on spectrum are smaller than main ordinary cases RQM NRQM. A straightforward limit our results mechanics shows present result is consistent what literature. We have seen term better other approximations finding approximate analytical solutions Klein-Gordon Manning–Rosen RNCQM NRNCQM.