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 that possess a unique (if any) quantized version. A simple criterion for the existence of such a quantized version is formulated. These mathematical results are then applied to the classical ``arrival time'' observable.