  A many--body Schr\"odinger equation for non--Abelian Chern--Simons particles
is obtained from both point--particle and field--theoretic pictures. We present
a particle Lagrangian and a field theoretic Lagrange density, and discuss their
properties. Both are quantized by the symplectic method of Hamiltonian
reduction. An $N$--body Schr\"odinger equation for the particles is obtained
from both starting points. It is shown that the resulting interaction between
particles can be replaced by non--trivial boundary conditions. Also, the
equation is compared with the one given in the literature.
