Hi Ed- My last answer was way too technical and short, a symptom of trying to work out my own understanding rather than trying to work out a good presentation for something I knew well.
Your question is pretty deep. Perhaps by "spin" you just mean the spatial part of the wave function. Spin is a very special property, which I should not have mentioned except for its role in the personal anecdote.
I think that this may be what you're working towards. The initial wave function of the system has some time dependence. In a slightly idealized case, it has a single frequency, i.e. the whole thing doesn't change except to rotate like e
-iωt in the complex plane. Now if anything physical is going to change, you need to have some slight spreading of the ω's (frequencies) of different components so that the interference patterns between them change. However, a very deep principle (Noether's theorem) says that the distribution of ω's itself doesn't change in a system where the rules are independent of time. By the way, those frequencies are just what we call "energies" after we multiply them by Planck's constant to put them in ordinary energy units.
Anyway, if the light and the non-light part part of the system (say of a molecule) are nearly independent, the frequency (energy) is about the sum of their separate contributions. So the frequency of the outgoing light has to be the difference between the frequency the molecule initially had and the one it ends up with. I think that's your point. I guess you can view conservation of energy as an interference effect: a starting state and an ending state with different frequencies have a rapidly oscillating overlap, destructively interfering over time.
What that doesn't say is why the light typically comes out as a single-lump photon, which then typically gets absorbed somewhere else as a single lump. Why not several photons, with the same net energy, which could then be absorbed separately in several places. This gets much deeper into the actual quantum details. Multi-photon effects do occur, but under most familiar circumstances are much rarer.
Mike W.
(published on 07/31/2012)