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

Varró, Sándor (2015) Regular phase operator and SU(1,1) coherent states of the harmonic oscillator. PHYSICA SCRIPTA, 90 (7). ISSN 0031-8949

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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 phase operator’ are SU(1,1) coherent states associated to the Holstein- Primakoff realization. In terms of these eigenstates the diagonal representation of phase densities and a generalized spectral resolution of the regular phase operator are derived, which suit very well to our intuitive pictures on classical phase-related quantities.

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