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

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