For a system composed of a cavity with a movable mirror(treated as a quantum harmonic oscillator with frequency ωm) and a single mode field in the cavity,the time evolution operator of the system is given,which is obtained by means of full quantum theory in the Schrdinger picture. The result shows that the state of the cavity field at the moment can give a variety of multicomponent Schrdinger cat states when the mirror returns to its original state,which are different from those in the published literature,and the desired Schrdinger cat state can be chosen by adjusting the frequency of the single mode cavity field.