  The information content of continuous quantum variables systems is usually
studied using a number of well known approximation methods. The approximations
are made to obtain the spectrum, eigenfunctions or the reduced density matrices
that are essential to calculate the entropy-like quantities that quantify the
information. Even in the sparse cases where the spectrum and eigenfunctions are
exactly known the entanglement spectrum, {\em i.e.} the spectrum of the reduced
density matrices that characterize the problem, must be obtained in an
approximate fashion. In this work, we obtain analytically a finite
representation of the reduced density matrices of the fundamental state of the
N-particle Calogero model for a discrete set of values of the interaction
parameter. As a consequence, the exact entanglement spectrum and von Neumann
entropy is worked out.
