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The Minimal Length and the Shannon Entropic Uncertainty Relation
Author
Source
Advances in High Energy Physics
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-04-17
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
In the framework of the generalized uncertainty principle, the position and momentum operators obey the modified commutation relation X,P=iħ1+βP2, where β is the deformation parameter.
Since the validity of the uncertainty relation for the Shannon entropies proposed by Beckner, Bialynicki-Birula, and Mycielski (BBM) depends on both the algebra and the used representation, we show that using the formally self-adjoint representation, that is, X=x and P=tanβp/β, where [x,p]=iħ, the BBM inequality is still valid in the form Sx+Sp≥1+lnπ as well as in ordinary quantum mechanics.
We explicitly indicate this result for the harmonic oscillator in the presence of the minimal length.
American Psychological Association (APA)
Pedram, Pouria. 2016. The Minimal Length and the Shannon Entropic Uncertainty Relation. Advances in High Energy Physics،Vol. 2016, no. 2016, pp.1-8.
https://search.emarefa.net/detail/BIM-1095208
Modern Language Association (MLA)
Pedram, Pouria. The Minimal Length and the Shannon Entropic Uncertainty Relation. Advances in High Energy Physics No. 2016 (2016), pp.1-8.
https://search.emarefa.net/detail/BIM-1095208
American Medical Association (AMA)
Pedram, Pouria. The Minimal Length and the Shannon Entropic Uncertainty Relation. Advances in High Energy Physics. 2016. Vol. 2016, no. 2016, pp.1-8.
https://search.emarefa.net/detail/BIM-1095208
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1095208