Space-time properties of free-motion time-of-arrival eigenfunctions

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Abstract
The properties of the time-of-arrival operator for free motion introduced by Aharonov and Bohm [Phys. Rev. 122, 1649 (1961)] and of its self-adjoint variants are studied. The domains of applicability of the different approaches are clarified. It is shown that the arrival time of the eigenfunctions is not sharply defined. However, strongly peaked real-space (normalized) wave packets constructed with narrow Gaussian envelopes centered on one of the eigenfunctions provide an arbitrarily sharp arrival time.
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