All l-state eigensolutions of the non-relativistic Schrodinger equation with the general molecular oscillator

In this study, we employ exact quantization rule (EQR) to derive the analytical approximate l-wave solutions of the Schrodinger equation with the general molecular oscillator (GMO). The energy eigenvalues equation and the corresponding wave -functions have been obtained explicitly. Improved Pekeris-type approximation Schemes have been used to deal with the orbital centrifugal term. We have deduced expressions for the bound-state energy eigenvalues of the Morse and shifted Deng-Fan oscillator as special cases of the GMO, and computed their resulting bound-state energy eigenvalues for H2, CO, HCl and LiH diatomic molecules. Our results are in good agreement with other results in the literature.