Weyl functions and their use in the study of quantum interference

Abstract

Weyl functions are shown to be an important tool in quantum phase-space studies. Their properties are studied and relations with other quantities are derived. The use of Weyl functions for the understanding of quantum interference phenomena is discussed. The general theory is applied to superpositions of $m$ coherent states uniformly distributed on a circle (generalized Schr\"odinger cats). The properties of these states are explored and their interference behavior is discussed, using Weyl functions.