Phys. Rev. A 72, 062107 (2005) [17 pages]Confined quantum time of arrival for the vanishing potentialSee Also: Erratum Received 27 June 2005; published 6 December 2005 We give full account of our recent report in E. A. Galapon, R. Caballar and R. Bahague Phys. Rev. Lett. 93 180406 (2004), where it is shown that formulating the free quantum time of arrival problem in a segment of the real line suggests rephrasing the quantum time of arrival problem to finding a complete set of states that evolve to unitarily arrive at a given point at a definite time. For a spatially confined particle, here it is shown explicitly that the problem admits a solution in the form of an eigenvalue problem of a class of compact and self-adjoint time of arrival operators derived by a quantization of the classical time of arrival. The eigenfunctions of these operators are numerically demonstrated to unitarily arrive at the origin at their respective eigenvalues. © 2005 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.72.062107
DOI:
10.1103/PhysRevA.72.062107
PACS:
03.65.Db
See AlsoErratum: Eric A. Galapon, Roland F. Caballar, and Ricardo Bahague, Erratum: Confined quantum time of arrival for the vanishing potential [Phys. Rev. A 72, 062107 (2005)], Phys. Rev. A 78, 049902 (2008). |
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