# Does measurement of momentum always collapse the wave function into a plane wave?

When you measure $$\vec p$$ the wave function collapses to an eigenstate of the momentum operator. These eigenfunctions are always plane waves, correct? Does it mean that momentum always collapses into a plane wave? What if the particle is confined in space? How can the wave function collapse into a function that is non-zero at infinity if the particle has zero probability of being found outside of the confined location?

• A minor addition to the good answer by @Emilio Pisanty: the reason we need to let the wavefunction expand before we can get a good momentum-measurement is because interactions are local in the spatial domain, not in the momentum domain. – Chiral Anomaly Mar 1 '19 at 18:55

When you measure $$\vec p$$ the wave function collapses to an eigenstate of the momentum operator. These eigenfunctions are always plane waves, correct? Does it mean that momentum always collapses into a plane wave?
To perform an accurate momentum measurement, regardless of what technique you use, you need to let the wavefunction expand to a given extent $$L$$, with the resolution of your momentum measurement getting fixed by the uncertainty principle at $$\Delta p \sim h/L$$. Performing a measurement of momentum to infinite precision is unphysical (exactly as with an infinite-precision measurement of position), but in the ideal case you would need to let the wavefunction expand to an unbounded size.