Five momenta

Abstract

A quantum or classical wavefunction depending on position can be associated with a local momentum in at least five apparently different ways: first, as the phase gradient of the wavefunction; second, as the local expectation value of the momentum operator; third, via the local current; fourth, via the Wigner phase-space distribution function; and fifth, as the weak value of momentum with position postselected. The different formulas are all equivalent, but give different insights into the underlying physics. Momenta one through three are largely familiar, but the fourth and fifth are less so.