Regular phase operator and SU(1,1) coherent states of the harmonic oscillator
arXiv:1412.3218 · doi:10.1088/0031-8949/90/7/074053
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
34 pages, 3 Figures
References in corpus (5)
- Entangled Photon-Electron States and the Number-Phase Minimum Uncertainty States of the Photon Field
- The canonical phase measurement is pure
- A New Look at the Quantum Mechanics of the Harmonic Oscillator
- Einstein's fluctuation formula. A historical overview
- Regular phase operator and SU(1,1) coherent states of the harmonic oscillator