This question already has an answer here:
After measuring a quantum state for a particular measurable, the state collapses to one of the eigenstate of that measurable. If we measure for momentum in an infinite square well, the system will collapse to a momentum eigenstate. But uncertainty in position is not arbitrary large (it's $2L$). So we are left with finite uncertainty in momentum and position at the same time. Does this mean that we aren't supposed to make such measurement? Or something else.