Energy spectra and expectation values of selected diatomic molecules through the solutions of Klein–Gordon equation with Eckart–Hellmann potential model

We solved the Klein–Gordon equation using the Nikiforov–Uvarov (NU) method with Eckart–Hellmann potential (EHP) model with approximation to the centrifugal term. The analytical expression of the ro-vibrational energy spectra in relativistic, non-relativistic and the corresponding normalised wavefunction were obtained. The numerical bound states energy for various screening parameters at different quantum states and ro-vibrational energies of EHP for VH, TiH, NiC, TiC and CuLi diatomicmolecules were computed. We have also obtained the expectation values of r−2, T and P2 using Hellmann–Feynman theorem for the selected diatomic molecules. Graphically, we have illustrated the variation of ro-vibrational energies and expectation values of r−2, T and P2. Four special cases of EHP where obtained and the results were in excellent agreements with the existing literature.