Exact solutions of nonrelativistic classical and quantum field theory with harmonic forces

Nonlinear field equations describing nonrelativistic particles interacting via harmonic forces are exactly solved. Collective variables of the system are identified and their evolution is found. Full quantum solution of the initial value problem is exhibited and compared with the classical solution of the same problem.To the memory of Marek Kac and Stanislaw marcin ulam - great scientists and our fine friends