  Having introduced the magnon in part I and the spinon in part II as the
relevant quasi-particles for the interpretation of the spectrum of low-lying
excitations in the one-dimensional (1D) s=1/2 Heisenberg ferromagnet and
antiferromagnet, respectively, we now study the low-lying excitations of the
Heisenberg antiferromagnet in a magnetic field and interpret these collective
states as composites of quasi-particles from a different species. We employ the
Bethe ansatz to calculate matrix elements and show how the results of such a
calculation can be used to predict lineshapes for neutron scattering
experiments on quasi-1D antiferromagnetic compounds. The paper is designed as a
tutorial for beginning graduate students. It includes 11 problems for further
study.
