Related papers: On some states minimizing uncertainty relations

On some states minimizing uncertainty relations

URL: http://arxiv.org/abs/2411.08131v1
Date: Tue, 12 Nov 2024 19:14:05 GMT
Title: On some states minimizing uncertainty relations
Authors: Krzysztof Urbanowski,
Abstract summary: We show that there can exist large set of states of the quantum system under considerations. These states are not eigenstates of either the observable $A$ or $B$. We also show that the so-called "sum uncertainty relations" also do not provide any information about lower bounds on the standard deviations calculated for these states.
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Abstract: Analyzing Heisenberg-Robertson (HR) and Schr\"{o}dinger uncertainty relations we found, that there can exist large set of states of the quantum system under considerations, for which the lower bound of product of the standard deviations of a pair of non-commuting observables, $A$ and $B$, is zero. These states are not eigenstates of either the observable $A$ or $B$. We have also shown that the so-called "sum uncertainty relations" also do not provide any information about lower bounds on the standard deviations calculated for these states.

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