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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 [arXiv : 1112.0523 (quant-ph)] by A. V. Dodonov and V. V. Dodonov. We believe that our method is simple and beautiful.

AN APPROXIMATE SOLUTION OF THE DYNAMICAL CASIMIR EFFECT IN A CAVITY WITH A TWO-LEVEL ATOM