  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.
