  A new convenient method to diagonalize the non-relativistic many-body
Schroedinger equation with two-body central potentials is derived. It combines
kinematic rotations (democracy transformations) and exact calculation of
overlap integrals between bases with different sets of mass-scaled Jacobi
coordinates, thereby allowing for a great simplification of this formidable
problem. We validate our method by obtaining a perfect correspondence with the
exactly solvable three-body ($N=3$) Calogero model in 1D.
