Complete Integrability in a Quantum Description of Chaotic Systems

For quantum bound systems whose classical versions are nonintegrable, coupled dynamical equations for both energy levels and eigenfunctions with a nonintegrability parameter $t$ taken as "time" are shown to be a completely integrable Calogero-Moser system in 1 + 1 dimensions with internal complex vector space. Lax forms and their complete algebraic solutions are given which, in place of statistical mechanics procedures, determine possible energy spectrum and wave-function patterns at an arbitrary value of $t$.