  From random matrix theory it is known that for special values of the coupling
constant the Calogero-Moser (CM) equation system is nothing but the radial part
of a generalized harmonic oscillator Schroedinger equation. This allows an
immediate construction of the solutions by means of a Rodriguez relation. The
results are easily generalized to arbitrary values of the coupling constant. By
this the CM equations become nearly trivial.
  As an application an expansion for <exp[i(XY)]> in terms of eigenfunctions of
the CM equation system is obtained, where X and Y are matrices taken from one
of the Gaussian ensembles, and the brackets denote an average over the angular
variables.
