The Garrison-Wong phase operator and the rotational covariance of phase states

•Properties of the Garrison-Wong phase operator are studied.•The eigenstates of an Hermitian phase operator are considered.•Phase distributions of truncated eigenstates of the operator have a dominant peak.

The cosine and sine phase operators and the Garrison-Wong (GW) operator of the phase have nonorthogonal diagonal representations in terms of the usual phase states. Also their orthogonal diagonal representations are studied theoretically. The phase distributions of the normalized truncated cosine and sine phase states reveal that the usual phase of the cosine and sine phase states is two-valued in general. The phase distributions of 110 normalized truncated GW phase states suggest that the usual phase of the GW phase states is single-valued. The preferred phases and phase dispersions of the normalized truncated GW phase states have been determined.