Question

Why doesn't there exist a statistical mechanics on wavefunction amplitudes?

Answer 1

It seems to me that if one cares about the particulars of the dynamics that is really going on, one would need to know the amplitudes very well, they determine how the system will evolve due to interference, so it would be important to speak of their probabilities as opposed to observable probabilities.

Answer 2

My guess is that it's because most of the states you derive in statistical mehcanics require the paritition function. Maybe since the partition function simply "counts" all possible configuration states, it doesn't care about quantum interference of these states....hmm..but what would the partition function for hong-ou-mandal