Using a recently developed method for calculating series expansions of
the excitation spectra of quantum lattice models, we obtain the spin-
wave spectra for square lattice, S=1/2 Heisenberg-Ising antiferromagne
ts. The calculated spin-wave spectrum for the Heisenberg model is clos
e to but noticeably different from a uniformly renormalized classical
(large-S) spectrum with the renormalization for the spin-wave velocity
of approximately 1.18. The relative weights of the single-magnon and
multiple-magnon contributions to neutron-scattering spectra are obtain
ed for wave vectors throughout the Brillouin zone.