Phys. Rev. A 72, 042107 (2005) [8 pages]Transition from discrete to continuous time-of-arrival distribution for a quantum particleReceived 8 August 2005; published 18 October 2005 We show that the Kijowski distribution for time of arrivals in the entire real line is the limiting distribution of the time-of-arrival distribution in a confining box as its length increases to infinity. The dynamics of the confined time-of-arrival eigenfunctions is also numerically investigated and demonstrated that the eigenfunctions evolve to have point supports at the arrival point at their respective eigenvalues in the limit of arbitrarily large confining lengths, giving insight into the ideal physical content of the Kijowsky distribution. © 2005 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.72.042107
DOI:
10.1103/PhysRevA.72.042107
PACS:
03.65.Db
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