The Minimal Length and the Shannon Entropic Uncertainty Relation. (17th April 2016)

• Record Type: Journal Article
• Authors: Pedram, Pouria
• Other Names: Majumder Barun Academic Editor.
• Is Part Of: Advances in high energy physics. Volume 2016(2016)
• Publication Date: 2016-04-17
• Subjects: Particles (Nuclear physics) -- Periodicals; Particles (Nuclear physics); Periodicals; 539.76
• DOI: 10.1155/2016/5101389
• Languages: English
• ISSNs: 1687-7357

Abstract

Abstract : In the framework of the generalized uncertainty principle, the position and momentum operators obey the modified commutation relationX, P = i ħ 1 + β P 2, whereβ 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 andP = tan ⁡ β p / β, where[ x, p ] = i ħ, the BBM inequality is still valid in the formS x + S p ≥ 1 + ln ⁡ π as well as in ordinary quantum mechanics. We explicitly indicate this result for the harmonic oscillator in the presence of the minimal length.