OK, let's say we have solved Schrodinger's eqn. for a system composed of a large number of degrees of freedom. We then start the wave-function off in an eigenstate of the nth energy level. It will never equilibrate- because the eigenstate is a stationary solution to S.E. Even if we use an arbitrary wavefunction at time t=0, the wavefunction can always be expanded as a linear superposition of stationary eigenstates. Sure, the phase of each eigenstate will change as a function of time- but there can never be a transition between eigenstates. So- is it possible at all for a closed quantum system to thermally equilibrate? If so- then how?