Quantum Solution of the Calogero System by the Projection Method

The projection method is a constructive proof of complete integrability of classical many-body systems. This method is extended to the quantum case. The wave functions and propagators of the $n$-particle Calogero systems are given in the form of integrals involving the wave functions and propagators of free motion in space of $n^2$ dimensions. Quantization of angular momentum in the large space yields solutions for discrete values of the coupling constant.