Abstract: The normal frequencies and its corresponding normal coordinates and conjugate momentums for a three-body coupled pendulum quantum system is derived in terms of the invariant eigen-operator method. With Hamiltonian of the system decoupled, the visible analytic solutions of normal frequencies in the system are obtained. The analytic solutions of exact wave function of the system in coordinate representation are deduced. Whereas, when calculating the Hamiltonian containing mechanical quantity with invariant eigen-operator method, the three power and more than three power terms of system Hamihonian are very intricacy.

Key words: invariant eigen-operator method, coupled pendulum quantum system, normal frequencies, analytic solutions of exact wave function