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Time in Quantum Mechanics pp 69–98Cite as

The Time-Energy Uncertainty Relation

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Part of the book series: Lecture Notes in Physics ((LNPMGR,volume 72))

Abstract

The time-energy uncertainty relation ΔT ΔE ≥ 1/2ħ (3.1) has been a controversial issue since the advent of quantum theory, with respect to appropriate formalisation, validity and possible meanings. Already the first formulations due to Bohr, Heisenberg, Pauli and Schrödinger are very different, as are the interpretations of the terms used. A comprehensive account of the development of this subject up to the 1980s is provided by a combination of the reviews of Jammer [1], Bauer and Mello [2], and Busch [3,4]. More recent reviews are concerned with different specific aspects of the subject: [5,6,7]. The purpose of this chapter is to show that different types of time energy uncertainty relation can indeed be deduced in specific contexts, but that there is no unique universal relation that could stand on equal footing with the position—momentum uncertainty relation. To this end, we will survey the various formulations of a time energy uncertainty relation, with a brief assessment of their validity, and along the way we will indicate some new developments that emerged since the 1990s (Sects. 3.3,3.4, and 3.6). In view of the existing reviews, references to older work will be restricted to a few key sources. A distinction of three aspects of time in quantum theory introduced in [3] will serve as a guide for a systematic classification of the different approaches (Sect. 3.2).

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Hull, Hull, UK

    Paul Busch

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  1. Paul Busch
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Editors and Affiliations

  1. Departamento de Química-Física Facultad de Ciencias, Universidad del País Vasco, Apdo. 644, Bilbao, Spain

    J. G. Muga

  2. Departamento de Física Fundamental II, Universidad de La Laguna, La Laguna (S/C de Tenerife), Spain

    R. Sala Mayato

  3. Fisika Teorikoaren Saila Zientzi Fakultatea, Euskal Herriko Unibertsitatea, 644 P.K., Bilbao, Spain

    I. L. Egusquiza

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© 2002 Springer-Verlag Berlin Heidelberg

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Busch, P. (2002). The Time-Energy Uncertainty Relation. In: Muga, J.G., Mayato, R.S., Egusquiza, I.L. (eds) Time in Quantum Mechanics. Lecture Notes in Physics, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45846-8_3

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  • DOI: https://doi.org/10.1007/3-540-45846-8_3

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  • Print ISBN: 978-3-540-43294-4

  • Online ISBN: 978-3-540-45846-3

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