An operational time of arrival is introduced using a realistic position and momentum measurement scheme. The phase-space measurement involves the dynamics of a quantum particle probed by a measuring device. For such a measurement an operational positive operator-valued measure in phase space is introduced and investigated. In such an operational formalism a quantum-mechanical time operator is constructed and analyzed. A phase-space time and energy uncertainty relation is derived.

• Received 28 September 1998

DOI:https://doi.org/10.1103/PhysRevA.60.2689