[tomyedwab]

That sounds more complicated than what is actually happening here. The way wave functions evolve over time, their velocity of movement is proportional to the frequency of oscillation. That is why measuring the frequency component of the wave function gives you the momentum function.

You have to keep in mind that the wave function represents the many places the particle can be with some probability, as well as the many frequencies it could have, so what uncertainty means in this case is that if you constrain the function to a small area in space (with zero probability outside it) you necessarily end up with a momentum function that spreads across many different velocities.