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The quantum absolute phase observable

Gilad Gour
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Abstract

Defining the observable ${\bf ϕ}$ 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 ${\bf Φ}\equiv |{\bfϕ}|$ by suitably restricting the Hilbert space of $x$ and $p$ like variables. This ${\bf Φ}$ 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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Gilad Gour. 2002-06-25. The quantum absolute phase observable. https://arxiv.org/abs/quant-ph/0102092

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