  The thermodynamical properties are calculated for a three-dimensional model
of $N$ harmonically interacting spin-polarized fermions in a parabolic
potential well. The obtained dependences of the chemical potential and of the
internal energy on the complete range of the temperature and of the number of
particles turn out to obey a scaling law, similar to the scaling from the
continuum approximation for the density of states. The calculation technique is
based on our path integral approach of symmetrized density matrices for
identical particles in a parabolic confining well.
