THE SYSTEM OF HARMONICALLY INTERACTING PARTICLES - AN EXACT SOLUTION OF THE QUANTUM-MECHANICAL PROBLEM

An original procedure has been developed to determine the eigenvalues and the eigenfunctions of quantum-mechanical many-body systems with a harmonic oscillator interaction. Exact solutions in the explicit form have been obtained for the case of systems containing three groups of identical particles. For the system containing two groups of identical particles, a solution in the adiabatic approximation has been obtained and compared with the exact one.