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 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.