  We obtain a time-evolution operator for a forced optomechanical quantum
system using Lie algebraic methods when the normalized coupling between the
electromagnetic field and a mechanical oscillator, $G/\omega_m$, is not
negligible compared to one. Due to the forcing term, the interaction picture
Hamiltonian contains the number operator in the exponents, and in order to deal
with it, we approximate these exponentials by their average values taken
between initial coherent states. Our approximation is justified when we compare
our results with the numerical solution of the number of photons, phonons,
Mandel parameter, and the Wigner function, showing an excellent agreement.
