Quasi-Classical Analysis of Coupled Oscillators

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Abstract
A set of harmonic oscillators is coupled for a certain time, after which the coupling is removed. The initial and final states of the set are expressed as superpositions of the coherent states of the uncoupled oscillators, as in Glauber's formalism. It is shown that the expansion kernel for the final state can be obtained approximately by substituting into the kernel for the initial state the classical equations of motion of the amplitudes of the oscillators. The evolution of a density operator for the system can be similarly calculated. The approximation is the more exact, the longer the time of interaction compared with the periods of the uncoupled oscillators.