Parametrically amplified radiation in a cavity with an oscillating wall

We introduce a time-dependent perturbation method to calculate the number of created particles in a 1D cavity with an oscillating wall of the frequency $\Omega . $ This method makes it easy to find the dominant part of the solution which results from the parametric resonance. The maximal number of particles are created at the mode frequency $\Omega/2 . $ Using the Floquet theory, we discuss the long-time behavior of the particle creation.