In CM, we have a prescription for measuring momentum. Velocity is defined, and we can measure it, and we can find out the momentum. Now, does quantum mechanics have the same prescription for measuring momentum (for a single free particle at least) ? I mean, for a single free particle, can we define a velocity operator first and define momentum operator as mass multiplied by that? We have this definition of momentum in quantum mechanics that it is the generator of translations. Roughly, all arguments regarding momentum seem to be logically deducible from that. Also, we know that in the classical limit, according to Ehrenfest's theorem, mean of the momentum evolves according to Newton's Law. But from these considerations, what can we say about the observable momentum's relation with the simple idea of momentum being something to do with how fast a particle moves. And how do we measure momentum in practice?