How to measure the momentum of single quanta

Abstract

The von Neumann theory of measurement, based on an entanglement of the quantum observable with a classical machine followed by decoherence or collapse, does not readily apply to most measurements of momentum. Indeed, how we measure the momentum of a quantum particle is not even discussed in most quantum mechanics textbooks. Instead, we often teach the lore that position and momentum cannot be measured at the same time. Yet, most ways to measure momentum actually involve measuring position to infer momentum. In this tutorial review, I examine real experiments that measure momentum and describe how one can improve our teaching of the theory of measurement when we focus on real experiments, rather than abstract mathematical models of measurement.