  We construct a theory of spin wave excitations in the bilayer manganite
La(1.2)Sr(1.8)Mn2O7 based on the simplest possible double-exchange model, but
including leading quantum corrections to the spin wave dispersion and damping.
Comparison is made with recent inelastic neutron scattering experiments. We
find that quantum effects account for some part of the measured damping of spin
waves, but cannot by themselves explain the observed softening of spin waves at
the zone boundary. Furthermore a doping dependence of the total spin wave
dispersion and the optical spin wave gap is predicted.
