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In this paper, we treat the so-called dynamical Casimir effect in a cavity with a two-level atom and give an analytic approximate solution under the general setting. The aim of the paper is to show another approach based on Mathematical Physics to the paper [Approximate analytical results on the cavity Casimir effect in the presence of a two-level atom, Phys. Rev. A85 (2012) 063804, arXiv: 1112.0523 [quant-ph]] by A. V. Dodonov and V. V. Dodonov. We believe that our method is simple and beautiful.
In this paper, we treat the Law's effective Hamiltonian of the dynamical Casimir effect (DCE) in a cavity and construct an analytic approximate solution of the time-dependent Schrödinger 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.