  We calculate the number of photons produced by the parametric resonance in a
cavity with vibrating walls. We consider the case that the frequency of
vibrating wall is $n \omega_1 (n=1,2,3,...)$ which is a generalization of other
works considering only $2 \omega_1$, where $\omega_1$ is the fundamental-mode
frequency of the electromagnetic field in the cavity. For the calculation of
time-evolution of quantum fields, we introduce a new method which is borrowed
from the time-dependent perturbation theory of the usual quantum mechanics.
This perturbation method makes it possible to calculate the photon number for
any $n$ and to observe clearly the effect of the parametric resonance.
