Physics – Quantum Physics
Scientific paper
2001-02-19
Physics
Quantum Physics
12 pages, REVTEX
Scientific paper
Defining the observable ${\bf \phi}$ canonically conjugate to the number observable ${\bf N}$ has long been an open problem in quantum theory. Here we show how to define the absolute phase observable ${\bf \Phi}\equiv |{\bf\phi}|$ by suitably restricting the Hilbert space of $x$ and $p$ like variables. This ${\bf \Phi}$ is actually the absolute value of the phase and has the correct classical limit. A correction to the ``cosine'' ${\bf C}$ and ``sine'' ${\bf S}$ operators of Carruthers and Nieto is obtained.
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