I know quantum mechanics is strange, but I'd like to think the strangeness is well defined. So can someone explain exactly what we mean when we talk about the momentum of a quantum particle? The reason I'm confused is that when the particle is in a position eigenstate, it has a definite position. If you take the measurement now, get a value, and then take it again later without disturbing the system in between, you'll get the same value. By heisenbergs principle, the uncertainty in momentum is infinite. But how can it be that there is any uncertainty in momentum when the particle is sitting perfectly still at the same spot? It's not moving, so what is this momentum it might have? Also, the usual qualitative way of describing uncertainty, (that you need to shine a very energetic photon to get an accurate position measurement, but that disturbs momentum, etc.) doesn't seem to make sense, because how can you disturb momentum but still maintain a fixed position? I know I must be thinking about momentum the wrong way, ie, too classically. Because mathematically, position and momentum are completely symmetrical in QM, but intuitively, momentum tells how the position is changing, but position is irrelevant to the momentum.