English

The Garrison-Wong quantum phase operator revisited

Quantum Physics 2020-08-21 v1

Abstract

We revisit the quantum phase operator Φ\Phi introduced by Garrison and Wong. Denoting by NN the number operator, we provide a detailed proof of the Heisenberg commutation relation ΦNNΦ=iI\Phi N - N\Phi = iI on the natural maximal domain D(ΦN)D(NΦ)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.

Cite

@article{arxiv.2008.08935,
  title  = {The Garrison-Wong quantum phase operator revisited},
  author = {Jan van Neerven},
  journal= {arXiv preprint arXiv:2008.08935},
  year   = {2020}
}
R2 v1 2026-06-23T17:59:20.051Z