Rotating Wave Approximation of the Law's Effective Hamiltonian on the Dynamical Casimir Effect

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.