Hi Rococo

To continue our discussion, you say that there should be destructive/constructive interference to always ensure unitarity, but what is wrong in me imagining say two gaussian wave packets with purely real phase. Actually for simplicity let's just use two delta functions. They are both real, and moving toward each other.

When they overlap their amplitude (such as it is for a delta-function, the coefficient in front) is double by linearity. You are saying this is impossible. Certainly this is counter-intuitive to me. My only interpretation can be that it is impossible to have two real delta functions moving toward each other.

I guess this makes sense, since if they are moving they have non-zero energy, and energy eigenfunctions rotate in the complex plane. So I guess what you are saying is that there is always a "conspiracy" such that the phases overlap in a way that unitarity is preserved. This just seems remarkable and unintuitive to me, since you can imagine purely real waves where this doesn't work.

It seems like there must be something deep here that I'm missing.