  The classical version of the three wave interaction models the creation and
destruction of waves; the quantized version models the creation and destruction
of particles. The quantum three wave interaction is described and the Bethe
Ansatz for the eigenfunctions is given in closed form. The Bethe equations are
derived in a rigorous fashion and are shown to have a thermodynamic limit. The
Dirac sea of negative energy states is obtained as the infinite density limit.
Finite particle/hole excitations are determined and the asymptotic relation of
energy and momentum is obtained. The Yang-Yang functional for the relative free
energy of finite density excitations is constructed and is shown to be convex
and bounded below. The equations of thermal equilibrium are obtained.
