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Phys. Rev. A 72, 042107 (2005) [8 pages]

Transition from discrete to continuous time-of-arrival distribution for a quantum particle

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Eric A. Galapon1,2,3 *, F. Delgado2, J. Gonzalo Muga2, and Iñigo Egusquiza3
1Theoretical Physics Group, National Institute of Physics, University of the Philippines, Diliman, Quezon City, 1101 Philippines
2Departamento de Química Física, UPV-EHU, Apdo. 644, 48080 Bilbao, Spain
3Theoretical Physics, The University of the Basque Country, Apdo. 644, 48080 Bilbao, Spain

Received 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

* Electronic address: eric.galapon@up.edu.ph

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