Operators of the phase. Fundamentals

Abstract

The asymptotic form of the Wigner function to a quantum operator is used to introduce a clear concept of the classical limit that is more than just a figure of speech. Quantum analogs of classical functions of the phase (or amplitude) variable in phase space are then identified. We study natural extrapolation procedures from the classical into the quantum regime, one of which is based upon writing the ladder operators as a product, in which one factor is a unitary quantum analog of the classical phase factor eiφ{symbol}′. The spectral decompositions of such unitary operators supply complete, orthogonal sets of states, each of which can be associated with a definite phase. © 1991.