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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.
Acta Physica Hungarica Series B, Quantum Electronics – Springer Journals
Published: Aug 29, 2009
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