  The properties of SU(1,1) SU(2),SU(2,1) and SU(3) have often been used in
quantum optics. In this paper we demonstrate the use of these symmetries. The
group properties of SU(1,1) SU(2), and SU(2,1) are used to find the transition
probabilities of various time dependent quadratic Hamiltonians. We consider
Hamiltonians representing the frequency converter,parametric amplifier and
raman scattering.These Hamiltonians are used to describe optical coupling in
nonlinear crystals.
