标题： 某些最小化不确定性关系的状态：对这些关系的新看法 显示英文标题

标题： On some states minimizing uncertainty relations: A new look at these relations

摘要： 分析海森堡-罗伯逊（HR）和薛定谔不确定性关系，我们发现，在所考虑的量子系统中，存在大量状态，这些状态下一对非对易可观测量$A$和$B$的标准偏差乘积的下限为零，并且这些状态与文献中描述的不同。 这些状态不是可观测量$A$或$B$的本征态。 在这些状态下，这些可观测量的相关函数等于零。 我们还证明了所谓的“和不确定性关系”也不提供关于这些状态下计算的标准偏差下限的任何信息。 我们进一步表明，不确定性原理在其最一般形式下有两个方面：一方面，它是标准偏差乘积的下限；另一方面，标准偏差的乘积是所考虑状态下一对非对易可观测量的相关函数模值的上限。 显示英文摘要

摘要： Analyzing Heisenberg--Robertson (HR) and Schr\"{o}dinger uncertainty relations we found, that there can exist a large set of states of the quantum system under considerations, for which the lower bound of the product of the standard deviations of a pair of non--commuting observables, $A$ and $B$, is zero, and which differ from those described in the literature. These states are not eigenstates of either the observable $A$ or $B$. The correlation function for these observables in such states is equal to zero. 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. We additionally show that the uncertainty principle in its most general form has two faces: one is that it is a lower bound on the product of standard deviations, and the other is that the product of standard deviations is an upper bound on the modulus of the correlation function of a pair of the non--commuting observables in the state under consideration.