Related papers: Uncertainty relations: curiosities and inconsistencies

Uncertainty relations: curiosities and inconsistencies

URL: http://arxiv.org/abs/2010.08339v1
Date: Tue, 13 Oct 2020 18:49:25 GMT
Title: Uncertainty relations: curiosities and inconsistencies
Authors: Krzysztof Urbanowski
Abstract summary: Analyzing general uncertainty relations one can find pairs of non-commuting observables $A$ and $B$ and such vectors that the lower bound for the product of standard deviations is zero: $Delta A,cdot,Delta Bgeq 0$. The status of the uncertainty relation in $cal PT$--symmetric quantum theory and the problems associated with it are also studied.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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 $\Delta A$ and $\Delta B$ calculated for these vectors is zero: $\Delta A\,\cdot\,\Delta B \geq 0$. 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 $(2\times 2)$ and $(3 \times 3)$ and the position--momentum uncertainty relation for a quantum particle in the box are considered. The status of the uncertainty relation in $\cal PT$--symmetric quantum theory and the problems associated with it are also studied.

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