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 $n{\omega }_1$ $(n=1,2,3,\dots ),$ 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 method that 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.

• Received 3 June 1997

DOI:https://doi.org/10.1103/PhysRevA.56.4440