Times of arrival: Bohm beats Kijowski

Abstract

We prove that the Bohmian arrival time of the 1D Schroedinger evolution violates the quadratic form structure on which Kijowski's axiomatic treatment of arrival times is based. Within Kijowski's framework, for a free right moving wave packet, the various notions of arrival time (at a fixed point x on the real line) all yield the same average arrival time. We derive an inequality relating the average Bohmian arrival time to the one of Kijowksi. We prove that the average Bohmian arrival time is less than Kijowski's one if and only if the wave packet leads to position probability backflow through x. Otherwise the two average arrival times coincide.

9 pages

References in corpus (3)

• A Survey on Bohmian Mechanics
• Time of Arrival from Bohmian Flow
• Bohmian arrival time without trajectories

Cited by in corpus (8)

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• Detection Time Distribution for Several Quantum Particles
• Diffraction in time of a confined particle and its Bohmian paths
• Double-slit experiment revisited
• Does the Heisenberg uncertainty principle apply along the time dimension?