Regular phase operator and SU(1,1) coherent states of the harmonic oscillator

Abstract

A new solution is proposed to the long-standing problem of describing the quantum phase of a harmonic oscillator. In terms of an'exponential phase operator', defined by a new 'polar decomposition' of the quantized amplitude of the oscillator, a regular phase operator is constructed in the Hilbert-Fock space as a strongly convergent power series. It is shown that the eigenstates of the new 'exponential operators are SU(1,1) coherent states in the Holstein-Primakoff realization. In terms of these eigenstates, the diagonal representation of phase densities and a generalized spectal resolution of the regular phase operator are derived, which suit very well to our intuitive pictures on classical phase-related quantities