TITLE: When does a wavefunction get re-created after a collapse?
QUESTION [0 upvotes]: Maybe another way of asking this would be, "When is decoherence un-done for a particle?"
Example:
Consider that we shoot an electron from a gun. Whilst in transit the electron is just a probability wave. At some point along it's path we make a measurement which collapses its wavefunction (decoherence). When does that electron ever become a probability wave again? Surely its wavefunction doesn't stay collapsed forever, or else everything in the universe would be collapsed at this point. So the question is, at what point in time, and what event/action, causes the electron to ever become probabilistic again, returning it to a state which is equivalent to when it was in transit before we made our measurement?
Another way of looking at the question would be: In the electron gun, the electron is bound to a proton, and collapsed. When, and what, makes it uncollapse when it is ejected from the proton and out of the gun, turning it back into pure probability?

REPLY [7 votes]: Let's say you measured the position of the electron exactly. While you might think that the electron has lost all it's quantum properties since it is localized in space and the wavefunction has collapsed, this is not true. This is because the collapse of the wavefunction depends intrinsically on the measurement that you are performing.
Let me clarify that statement. I presume you're in some sense familiar with the uncertainty principle. Informally, the more localized a particle is in space, the more spread you have in the momenta and vice versa. By measuring the position exactly, we get a wavefunction that is completely localized in the position basis, but completely unlocalized in the momentum basis! So by collapsing the wavefunction, we actually get something that is not classical at all from the momentum point of view.
So to answer your question, the collapse of a wavefunction is only the abrupt change to an (eigen)state of your measurement, it never stops being a wavefunction. For that reason, the wavefunction will just evolve according to the Schrödinger equation after the measurement, and there is no real physical distinction between a collapsed and uncollapsed wavefunction; as most things in quantum mechanics, it all depends on the basis that you use to look at a problem.
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