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International Journal of Modern Physics E

TIME-OF-ARRIVAL OPERATOR WITHIN SPACE-TIME APPROACH TO QUANTUM MECHANICS

M. DȨBICKI, ANDRZEJ GÓŹDŹ

Published Feb 20, 2006• 7 citations
Publisher

Abstract

In this paper we consider the time as a dynamical variable. In particular we apply the time operator to an example of the particle arrival problem within two-dimensional space–time.
DOI
10.1142/s0218301306004326

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We present a decomposition of the general quantum-mechanical evolution operator that corresponds to the path decomposition expansion, and interpret its constituents in terms of the quantum Zeno effect (QZE). This decomposition is applied to a finite-dimensional example and to the case of a free particle in the real line, where the possibility of boundary conditions more general than those hitherto considered in the literature is shown. We reinterpret the assignment of consistent probabilities to different regions of space-time in terms of the QZE. The comparison of the approach of consistent histories to the problem of time of arrival with the solution provided by the probability distribution of Kijowski shows the strength of the latter point of view.