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So let's say I have a machine that measures the position very very precisely. Then the uncertainty of this non-moving particles momentum reach infinity, the momentum could have big magnitude. But how can a particle that don't move have momentum? Or does the particle oscillate with a de broglie wavelength within the discrete finite volume we have measured it to be within (because we can not measure exactly)?

Or does the uncertainty principle don't apply once measurement is done? It just tells uncertainty if I "would" make a measurement?

Feel free to go complex on me.