量子相位问题：迈向解决的步骤
The quantum phase problem: steps toward a resolution
摘要：
定义可观测${\bf ϕ}$与可观测数${\bf N}$正则共轭一直是量子理论中的一个开放问题。这个问题源于${\bf N}$是从下面有界的。在以前的工作中，我们已经展示了如何定义的绝对相位观测${\bf Φ}\equiv |{\bfϕ}|$适当限制的希尔伯特空间的$x$和$p$一样的变量。在这里，我们表明，也从经典的角度来看，没有严格的定义，即使它的绝对值是很好的定义的相位。
英文摘要：
Defining the observable ${\bf ϕ}$ canonically conjugate to the number observable ${\bf N}$ has long been an open problem in quantum theory. The problem stems from the fact that ${\bf N}$ is bounded from below. In a previous work we have shown how to define the absolute phase observable ${\bf Φ}\equiv |{\bfϕ}|$ by suitably restricting the Hilbert space of $x$ and $p$ like variables. Here we show that also from the classical point of view, there is no rigorous definition for the phase even though it's absolute value is well defined.
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