We present a method to solve exactly a one-dimensional model of quantized r
adiations in a cavity oscillating in the fundamental resonance, using the e
ffective Hamiltonian derived by C. K. Law [Phys. Rev. A 49, 433 (1994)]. Wi
th this method. we derived explicit analytical expressions for the diagonal
ized Hamiltonian, the time-varying annihilation, creation, and photon numbe
r operators for the radiation field, which completely specify the dynamics
of the system. [S1050-2947(99)00604-6].