Measuring "Velocity" in Quantum Mechanics: Meaning of the p/m Operator

[bob900]

Classically, a direct measurement of velocity requires two measurements - position at time t1 and position at time t2. In QM such a measurement is not meaningful, since measuring position at time t1 would necessarily affect the particle (i.e. cause it to collapse to some position eigenstate).

How would one make a measurement of velocity in QM? You would need to measure it using only a single measurement (corresponding to the p/m = operator) on a particle's state ψ. But what meaning can we assign to the result of such a measurement? Certainly not the classical concept of velocity which tells us where the particle will be after some short period of time Δt, since we can't tell the particle's future position after our measurement of its p/m 'velocity'. So in what sense can we even refer to it as 'velocity', when in reality we are measuring something completely distinct from that classical concept?

 

[Drakkith]

I believe the measurement would disturb the particle, but only by a certain amount. Your measurements would be constrained by some amount of uncertainty. Just because the wavefunction collapses doesn't mean we cannot make predictions about where it will be in the future, it is only that those predictions are limited in their accuracy and precision.