论文标题
重新审视的不确定性原则
The Uncertainty Principle Revisited
论文作者
论文摘要
我们研究了两个可观察的$ \ hat {a} $和$ \ hat {b} $连续测量的量子力学不确定性关系，分别在同一系统上执行。我们使用von Neumann测量模型的扩展，其中两个探针在连续两个时间内与适当的同一系统相互作用，因此我们可以展示第一种相互作用的令人不安的效果如何影响第二个测量。检测第二个{\ em Probe}的统计属性$ q_2 $在第一个{\ em probe}测量的条件下，产生$ q_1 $，我们获取有关{\ em System}变量$ b_m的统计分布的信息，条件是在$ a_n $中以$ $ $ $δ$Δa$ nike $ a_n $ a_n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $Δ此统计分布作为$ΔA$的函数的宽度构成{\ em不确定性关系}。我们发现这种不确定性关系与已连续测量的两个可观察到的换向器的一般联系。我们说明了在离散和连续情况下以及模型中连续测量位置和动量的连续测量的关系，以连续测量更通用的可观察类别类别。
We study the quantum-mechanical uncertainty relation originating from the successive measurement of two observables $\hat{A}$ and $\hat{B}$, with eigenvalues $a_n$ and $b_m$, respectively, performed on the same system. We use an extension of the von Neumann model of measurement, in which two probes interact with the same system proper at two successive times, so we can exhibit how the disturbing effect of the first interaction affects the second measurement. Detecting the statistical properties of the second {\em probe} variable $Q_2$ conditioned on the first {\em probe} measurement yielding $Q_1$ we obtain information on the statistical distribution of the {\em system} variable $b_m$ conditioned on having found the system variable $a_n$ in the interval $δa$ around $a^{(n)}$. The width of this statistical distribution as function of $δa$ constitutes an {\em uncertainty relation}. We find a general connection of this uncertainty relation with the commutator of the two observables that have been measured successively. We illustrate this relation for the successive measurement of position and momentum in the discrete and in the continuous cases and, within a model, for the successive measurement of a more general class of observables.
