  We show that the interaction between a movable mirror with a quantized field
that interacts with a two-level atom may be simplified via a transformation
that involves Susskind-Glogower operators (SGO). By using this transformation
it is easy to show that we can cast the Hamiltonian, after a series of small
rotations, into an effective Hamiltonian that may be solved. We would like to
stress that the transformation in terms of SGO already simplifies enough the
Hamiltonian in the sense that, in an exact way, it "eliminates" one of the
three-subsystems, namely the quantized field.
