New representation of the multimode phase shifting operator and its application

Based on the rotation transformation in phase space andthe technique of integration within an ordered product of operators,the coherent state representation of the multimode phase shiftingoperator and one of its new applications in quantum mechanics aregiven. It is proved that the coherent state is a natural languagefor describing the phase shifting operator or multimode phaseshifting operator. The multimode phase shifting operator is alsoa useful tool to solve the dynamic problems of the multimodecoordinate--momentum coupled harmonic oscillators. The exact energyspectra and eigenstates of such multimode coupled harmonicoscillators can be easily obtained by using the multimode phaseshifting operator.