  This work is devoted to the study of some exactly solvable quantum problems
of four, five and six bodies moving on the line. We solve completely the
corresponding stationary Schr\"odinger equation for these systems confined in
an harmonic trap, and interacting pairwise, in clusters of two and three
particles, by two-body inverse square Calogero potential. Both translationaly
and non-translationaly invariant multi-body potentials are added. In each case,
the full solutions are provided, namely the normalized regular eigensolutions
and the eigenenergies spectrum. The irregular solutions are also studied. We
discuss the domains of coupling constants for which these irregular solutions
are square integrable. The case of a "Coulomb-type" confinement is investigated
only for the bound states of the four-body systems.
