Interpretation of quantum and classical angular momentum polarization moments

This Letter presents a derivation of the relationship between the quantum and classical descriptions of angular momentum polarization. The results involve an uncertainty broadening term that directly expresses the restrictions imposed by the uncertainty principle. It is argued that neglect of this term can lead to error in the interpretation of theoretical or experimental angular momentum polarization data. Functions that take the uncertainty broadening into account, appropriate for use in quantum or quasiclassical descriptions of spatial distributions of angular momenta, are defined.