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arXiv · 2008.08935

The Garrison-Wong quantum phase operator revisited

Jan van Neerven
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Abstract

We revisit the quantum phase operator $\Phi$ introduced by Garrison and Wong. Denoting by $N$ the number operator, we provide a detailed proof of the Heisenberg commutation relation $\Phi N - N\Phi = iI$ on the natural maximal domain $D(\Phi N) \cap D(N \Phi)$ as well as the failure of the Weyl commutation relations, and discuss some further interesting properties of this pair.

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Jan van Neerven. 2020-08-20. The Garrison-Wong quantum phase operator revisited. https://arxiv.org/abs/2008.08935

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