In the interaction representation, the time-dependent quantum calculation formulas for the atom-oscillator scattering are derived by using angular momentum coupling theory, and the vibrational and rotational transition probabilities and the partial cross sections for the He-H2 system are calculated. The results show that: (1) the interaction picture wave function is highly localized in coordinate space and varies slowly in time, therefore, we are able to obtain higher accuracy in calculating scattering quantities, and the calculated results are in excellent agreement with that of CC method; (2) the effect of the vibration term on the calculating time is dependent upon the integration of the potential matrix, in which a calculation including only the ground state gives remarkably good results.