  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.
