- #1
christianjb
- 529
- 1
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?
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?