Times of arrival: Bohm beats Kijowski

Michael Ruggenthaler, Gebhard Grübl and Sabine Kreidl

Institut für Theoretische Physik der Universität Innsbruck
Technikerstr. 25, A-6020 Innsbruck, Austria

Gebhard.Gruebl@uibk.ac.at

Submitted April 25, 2005


Abstract. We prove that the Bohmian arrival time of the 1D Schrödinger 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 tex2html_wrap_inline39, the various notions of arrival time (at a fixed point x on the real line) all yield the same average arrival time tex2html_wrap_inline43. We derive the inequality tex2html_wrap_inline45 relating the average Bohmian arrival time to the one of Kijowksi. We prove that tex2html_wrap_inline47 if and only if tex2html_wrap_inline39 leads to position probability backflow through x.

Published 14 September 2005.

J. Phys. A: Math. Gen. 38, 8445 - 8451 (2005).

Preprint. http://arXiv.org/abs/quant-ph/0504185, 9 pages, 137 kB.

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