Factorization of analytic representations in the unit disc and number-phase statistics of a quantum harmonic oscillator
Apostol Vourdas, Constantin Brif, Adrian B. Mann · Journal of Physics A Mathematical and General · 1996
The inner - outer part factorization of analytic representations in the unit disc is used for an effective characterization of the number-phase statistical properties of a quantum harmonic oscillator. It is shown that the factorization is intimately connected with the number-phase Weyl semigroup and its properties. In the Barut - Girardello analytic representation the factorization is implemented as a convolution. Several examples are given which demonstrate the physical significance of the factorization and its role for quantum statistics. In particular, we study the effect of phase-space interference on the factorization properties of a superposition state.