Kechrimparis, Spyridon and Weigert, Stefan Ludwig Otto orcid.org/0000-0002-6647-3252 (2017) Geometry of Uncertainty Relations for Linear Combinations of Position and Momentum. Journal of Physics A: Mathematical and Theoretical. 025303. ISSN 1751-8113
Abstract
For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by N linear combinations of position and momentum observables. The bounds depend on their degree of incompatibility defined by the area of a parallelogram in an N-dimensional coefficient space. Maximal incompatibility occurs if the observables give rise to regular polygons in phase space. We also conjecture a Hirschman-type uncertainty relation for N observables linear in position and momentum, generalizing the original relation which lower-bounds the sum of the position and momentum Shannon entropies of the particle.
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 IOP Publishing Ltd. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details |
Dates: |
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Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Mathematics (York) |
Depositing User: | Pure (York) |
Date Deposited: | 27 Nov 2017 16:40 |
Last Modified: | 06 Dec 2023 12:10 |
Published Version: | https://doi.org/10.1088/1751-8121/aa9cfc |
Status: | Published |
Refereed: | Yes |
Identification Number: | https://doi.org/10.1088/1751-8121/aa9cfc |
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