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In this paper we treat the Law's effective Hamiltonian of the Dynamical Casimir Effect in a cavity and construct an analytic approximate solution of the time-dependent Schr{\"o}dinger equation under the general setting through a kind of rotating wave approximation (RWA). To the best of our knowledge this is the finest analytic approximate solution.

ROTATING WAVE APPROXIMATION OF THE LAW'S EFFECTIVE HAMILTONIAN ON THE DYNAMICAL CASIMIR EFFECT