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-Hell mann 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 diatomic-molecules were computed. We have also obtained the expectation values of < r(-2)>, < T > and < P-2 > 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 < P-2 >. Four special cases of EHP where obtained and the results were in excellent agreements with the existing literature. [GRAPHICS]