CANONICAL-TRANSFORMATIONS TO ACTION AND PHASE-ANGLE VARIABLES AND PHASE OPERATORS

The well-known difficulties of defining a phase operator of an oscilla tor are considered from the point of view of the canonical transformat ion to action and phase-angle variables. This transformation turns out to be nonbijective, i.e., it is not a one-to-one onto mapping. In ord er to make possible the unitarity of its representations in quantum op tics we should enlarge the Hilbert space of the problem. In this enlar ged space we find a phase operator that, after projection, reproduces previous candidates to represent a well-behaved phase operator in the quantum domain.