The Garrison-Wong quantum phase operator revisited

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.