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Advances in High Energy Physics
Volume 2016, Article ID 5101389, 8 pages
http://dx.doi.org/10.1155/2016/5101389
Research Article

The Minimal Length and the Shannon Entropic Uncertainty Relation

Department of Physics, Islamic Azad University, Science and Research Branch, Tehran 1477893855, Iran

Received 5 January 2016; Accepted 13 March 2016

Academic Editor: Barun Majumder

Copyright © 2016 Pouria Pedram. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Abstract

In the framework of the generalized uncertainty principle, the position and momentum operators obey the modified commutation relation , where 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, and , where , the BBM inequality is still valid in the form as well as in ordinary quantum mechanics. We explicitly indicate this result for the harmonic oscillator in the presence of the minimal length.