Quantum kinetic energy densities: an operational approach

We propose and investigate a procedure to measure, at least in principle, a positive quantum version of the local kinetic energy density. This procedure is based, under certain idealized limits, on the detection rate of photons emitted by moving atoms which are excited by a localized laser beam. The same type of experiment, but in different limits, can also provide other non-positive-definite versions of the kinetic energy density. A connection with quantum arrival time distributions is discussed.