  We consider energetics and structural properties of a many particle system in
one dimension with pairwise contact interactions confined in a parabolic
external potential. To render the problem analytically solvable, we use the
harmonic approximation scheme at the level of the Hamiltonian. We investigate
the scaling with particle number of the ground state energies for systems
consisting of identical bosons or fermions. We then proceed to focus on bosonic
systems and make a detailed comparison to known exact results in the absence of
the parabolic external trap for three-body systems. We also consider the
thermodynamics of the harmonic model which turns out to be similar for bosons
and fermions due to the lack of degeneracy in one dimension.
