论文标题
不确定性关系：好奇心和不一致之处
Uncertainty relations: curiosities and inconsistencies
论文作者
论文摘要
分析一般的不确定性关系可以发现，可以存在这样的非公认可观察的$ a $ a $和$ b $以及这些向量$ΔA$和$ΔB$的下限的向量，这些向量是零：$ΔA\，\ cdot \ cdot \，cd cdot \，Δb，δb\ geq 0 $。在这里，我们讨论了此类案例和其他一些矛盾的示例，在某些特殊情况下，可以发现对不确定性关系进行严格分析。作为此类情况的说明，考虑了包装盒中量子粒子的量子 - momentum不确定性关系的位置。还研究了$ \ cal pt $中的不确定性关系的状态 - 对称量子理论及其相关的问题。
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: $ΔA\,\cdot\,ΔB \geq 0$. 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.
