The problem of the quantum vacuum in a one-dimensional cavity is discussed. We put forward a new method to solve Moore's equation and search for fundamental classical basis. This new method is applicable to problems with general wall trajectories and enables us to calculate both phase functions and their derivatives by iterations. We calculate energy densities and total energies for oscillating cavities. In particular, off resonant motions are studied.

PACS numbers: 11.10.--z, 03.70.+k