Angular momenta dynamics in magnetic and electric field: Classical and quantum approach

A standard description of the angular momentum in atomic or molecular physics is based on quantum mechanics. However, especially at large angular-momentum limit in molecules, sometimes a classical approach greatly simplifies problems that are extremely complicated from a quantum-mechanical viewpoint. The aim of this paper is to examine the relationship between the classical and quantum descriptions of the angular-momentum distribution in an ensemble of particles. At first glance, quantum and classical approaches appear to be absolutely different and have very little in common. In this paper this relationship is analyzed. It is shown that similarities can be found between the precession of angular momentum in the external field and the influence of this field upon the wave-function phase of a microparticle. The importance of wave function phases is stressed even for stationary conditions, and some examples of coherent superposition of quantum states are presented. The general method of how to pass from the quantum approach to a classical one is formulated. Results are visualized in the form of 3D distribution functions. This approach allows a graphical interpretation and thus results in a better understanding, sometimes at first glance, of counterintuitive quantum results. As an example the phenomenon of alignment-orientation transition is considered. Rather than presenting only formal derivations, the emphasis is on the instructional aspects, and on illustrating the general approach.