Factorization of wave functions of the quantum integrable particle systems

The relation between the characteristics of the equilibrium configurations of the classical Calogero-Moser integrable systems and properties of the ground state of their quantum analogs is found. It is shown that under the condition of factorization of the wave function of these systems the coordinates of classical particles at equilibrium are zeroes of the polynomial solutions of the second-order linear differential equation. It turns out that, under these conditions, the dependence of classical and quantum minimal energies on the parameters of the interaction potential is the same.