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We calculate the number of photons produced by the parametric resonance in acavity with vibrating walls. We consider the case that the frequency ofvibrating wall is $n \omega_1 (n=1,2,3,...)$ which is a generalization of otherworks considering only $2 \omega_1$, where $\omega_1$ is the fundamental-modefrequency of the electromagnetic field in the cavity. For the calculation oftime-evolution of quantum fields, we introduce a new method which is borrowedfrom the time-dependent perturbation theory of the usual quantum mechanics.This perturbation method makes it possible to calculate the photon number forany $n$ and to observe clearly the effect of the parametric resonance.Comment: 15 pages, RevTeX, no figure

Production of photons by the parametric resonance in the dynamical Casimir effect