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Open AccessArticle

Uncertainty Relations: Curiosities and Inconsistencies

Institute of Physics, University of Zielona Góra, ul. Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland
Symmetry 2020, 12(10), 1640; https://doi.org/10.3390/sym12101640
Received: 17 August 2020 / Revised: 16 September 2020 / Accepted: 22 September 2020 / Published: 6 October 2020
(This article belongs to the Special Issue PT-Symmetry in Physical Systems)
Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables A and B and such vectors that the lower bound for the product of standard deviations ΔA and ΔB calculated for these vectors is zero: ΔA·ΔB0. Here we discuss examples of such cases and some other inconsistencies which can be found performing a rigorous analysis of the uncertainty relations in some special cases. As an illustration of such cases matrices (2×2) and (3×3) and the position–momentum uncertainty relation for a quantum particle in the box are considered. The status of the uncertainty relation in PT–symmetric quantum theory and the problems associated with it are also studied. View Full-Text
Keywords: uncertainty relations; uncertainties in PT –symmetric quantum mechanics uncertainty relations; uncertainties in PT –symmetric quantum mechanics
MDPI and ACS Style

Urbanowski, K. Uncertainty Relations: Curiosities and Inconsistencies. Symmetry 2020, 12, 1640.

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