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I have a quick question regarding the relationship between the uncertainty principle and the measurement postulate. According to the former, the higher our certainty is about the position of a particle, the lower our certainty is regarding its momentum, and vice versa. This means that our uncertainty about the momentum would be maximum if we knew the position of the particle exactly. Now, according to the measurement postulate, if we made a measurement and found the particle at a particular position, the wave function will collapse into a delta function, which means that the probability distribution for the position of the particle is now just that delta function. Furthermore, we know that if we were to measure its position again a very short time after the first measurement, we are bound to find the particle at the same position (the wave function remains collapsed for some small amount of time).

But this is where I'm confused. If we know where the particle is now and that we are going to find it at the exact same position after some short Δt, doesn't this mean that the particle just hasn't moved at all and therefore its momentum must be zero? Clearly this can't be true, since that would mean we know both the position and the momentum exactly.

I would really appreciate clarifying comments!

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# The uncertainty principle and the measurement postulate

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