Arrival time in quantum mechanics (demonstrated in geometrical order)

Abstract

A geometric construction of the arrival time in conventional quantum mechanics is presented. It is based on a careful mathematical analysis of different quantization procedures for classical observables as functions of positions and momenta. A class of observables is selected which possess a unique (if any) quantized version. A simple criterion for existence of such a quantized version is formulated. These mathematical results are then applied to the classical "arrival time" observable.