Evaluation of the bound state energies of some diatomic molecules from the approximate solutions of the Schrodinger equation with Eckart plus inversely quadratic Yukawa potential.

We have obtained analytically the bound state solutions for the non-relativistic Schrodinger equation for the Eckart plus inversely quadratic Yukawa potential (EIQYP) using the parametric Nikiforov-Uvarov (NU) method. In order to validate our approximation, the bound state energies were computed and predicted for some selected diatomic molecules at different adjustable screening parameters from the available spectroscopic model parameters. The fact-finding obtained are in agreement with previously reported results available in literature. Furthermore, the graphs of the effective potential against inter-nuclear distance for low and high values of the screening parameters were reported. From our graphs, we observed that the approximation is best fit for very low values of the screening parameter α ≪ 1.