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Time of arrival in the wigner phase space formulation of quantum mechanics

Time of arrival in the wigner phase space formulation of quantum mechanics An expression for the average time of arrival of a free particle, to a given small part of space, is derived using the Wigner phase space formulation of quantum mechanics. Special care is paid to the case of the one-dimensional motion. It is shown that infinite values for average times of arrival, which arise in this case when one applies Wigner’s approach in a formally direct way, are mathematical artifacts and the way to avoid them is proposed. Asymptotic behavior of the time of arrival of a particle initially in a coherent state, to the origin of the coordinate system, is analyzed. It is shown that the leading term is given by the ratio of the average value of coordinate and average value of velocity, around which the considered coherent state is centered. The obtained results are discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Physica Hungarica Series B, Quantum Electronics Springer Journals

Time of arrival in the wigner phase space formulation of quantum mechanics

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References (15)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Akadémiai Kiadó
Subject
Physics; Nuclear Physics, Heavy Ions, Hadrons
ISSN
1589-9535
eISSN
1786-3767
DOI
10.1556/APH.26.2006.3-4.5
Publisher site
See Article on Publisher Site

Abstract

An expression for the average time of arrival of a free particle, to a given small part of space, is derived using the Wigner phase space formulation of quantum mechanics. Special care is paid to the case of the one-dimensional motion. It is shown that infinite values for average times of arrival, which arise in this case when one applies Wigner’s approach in a formally direct way, are mathematical artifacts and the way to avoid them is proposed. Asymptotic behavior of the time of arrival of a particle initially in a coherent state, to the origin of the coordinate system, is analyzed. It is shown that the leading term is given by the ratio of the average value of coordinate and average value of velocity, around which the considered coherent state is centered. The obtained results are discussed.

Journal

Acta Physica Hungarica Series B, Quantum ElectronicsSpringer Journals

Published: Aug 29, 2009

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