Confined Quantum Time of Arrival for Vanishing Potential
Abstract
We give full account of our recent report in [E.A. Galapon, R. Caballar, R. Bahague {\it Phys. Rev. Let.} {\bf 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 unitarilly arrive at the origin at their respective eigenvalues.
Cite
@article{arxiv.quant-ph/0512096,
title = {Confined Quantum Time of Arrival for Vanishing Potential},
author = {Eric A. Galapon and Roland F. Caballar and Ricardo Bahague},
journal= {arXiv preprint arXiv:quant-ph/0512096},
year = {2009}
}
Comments
accepted for publication in Phys. Rev. A