From the Weyl quantization of a particle on the circle to number-phase Wigner functions

Maciej Przanowski; Przemyslaw Brzykcy; Jaromir Tosiek

doi:10.1016/j.aop.2014.10.011

paper

From the Weyl quantization of a particle on the circle to number-phase Wigner functions

arXiv:1311.7335 · doi:10.1016/j.aop.2014.10.011

Abstract

A generalized Weyl quantization formalism for a particle on the circle investigated in \cite{1} is developed. A Wigner function for the state $ϱ^$ and the kernel $K$ for a particle on the circle is defined and its properties are analyzed. Then it is shown how this Wigner function can be easily modified to give the number-phase Wigner function in quantum optics. Some examples of such number-phase Wigner function are considered.

22 pages, 6 figures