Almost-periodic time observables for bound quantum systems

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Title Almost-periodic time observables for bound quantum systems
Author Hall, Michael
Journal Name Journal of Physics A
Year Published 2008
Place of publication United Kingdom
Publisher Institute of Physics Publishing Ltd.
Abstract It is shown that a canonical time observable may be defined for any quantum system having a discrete set of energy eigenvalues, thus significantly generalizing the known case of time observables for periodic quantum systems (such as the harmonic oscillator). The general case requires the introduction of almost-periodic probability operator measures (POMs), which allow the expectation value of any almost-periodic function to be calculated. An entropic uncertainty relation for energy and time is obtained which generalizes the known uncertainty relation for periodic quantum systems. While non-periodic quantum systems with discrete energy spectra, such as hydrogen atoms, typically make poor clocks that yield no more than 1 bit of time information, the anisotropic oscillator provides an interesting exception. More generally, a canonically conjugate observable may be defined for any Hermitian operator having a discrete spectrum.
Peer Reviewed Yes
Published Yes
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Copyright Statement Copyright 2008 Institute of Physics Publishing. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher.Please refer to the journal's website for access to the definitive, published version.
Volume 41
Issue Number 25
Page from 255301-1
Page to 255301-14
ISSN 1751-8113
Date Accessioned 2011-12-05
Language en_US
Research Centre Centre for Quantum Dynamics
Faculty Faculty of Science, Environment, Engineering and Technology
Subject Algebraic Structures in Mathematical Physics; Quantum Information, Computation and Communication; Quantum Physics
Publication Type Journal Articles (Refereed Article)
Publication Type Code c1x

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