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For $N$-coupled generalized time-dependent oscillators, primary invariantsand a generalized invariant are found in terms of classical solutions. Exactquantum motions satisfying the Heisenberg equation of motion are also found.For number states and coherent states of the generalized invariant, theuncertainties in positions and momenta are obtained.Comment: 8 pages, revTe

Heisenberg picture approach to the invariants and the exact quantum motions for coupled parametric oscillators