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  • Almost-periodic time observables for bound quantum systems

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    74569_1.pdf (163.7Kb)
    Author(s)
    Hall, Michael JW
    Griffith University Author(s)
    Hall, Michael J.
    Year published
    2008
    Metadata
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    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 ...
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    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.
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    Journal Title
    Journal of Physics A
    Volume
    41
    Issue
    25
    DOI
    https://doi.org/10.1088/1751-8113/41/25/255301
    Copyright Statement
    © 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.
    Subject
    Mathematical sciences
    Algebraic structures in mathematical physics
    Physical sciences
    Quantum information, computation and communication
    Quantum physics not elsewhere classified
    Publication URI
    http://hdl.handle.net/10072/42710
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    • Journal articles

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