Spatial distributions of angular momenta in quantum and quasiclassical stereodynamics

We have recently reported a derivation of the relationship between the quantum and classical descriptions of angular momentum polarization [M. P. de Miranda and F. Javier Aoiz, Phys. Rev. Lett. 93, 083201 (2004)]. This paper presents a detailed account of the derivation outlined in that paper, and discusses the implications of the new results. These include (i) a new expression of the role of the uncertainty principle in the broadening of angular momentum distributions, (ii) the attribution of azimuthal fluctuations of angular momentum distributions to spatial quantum beats, (iii) the definition of a new Fourier transform of the density matrix, distinct from those suggested in the past, that provides an alternative view of how the quantum description of angular momentum polarization approaches the classical one in the correspondence principle limit, (iv) a prescription for the determination of a quasiclassical angular momentum distribution function that does not suffer from problems encountered with its purely classical counterpart, and (v) a description of how angular momentum distributions commonly visualized with recourse to the classical vector model can be depicted with exact and well-defined quantum mechanics.