Wigner density of a rigid rotator

Abstract

We show that the Wigner density of the rigid rotator, in an appropriate, i.e., four-dimensional, phase space, is positive. This result holds in the ground state (S state), and also in the thermal mixture state at all finite temperatures. We discuss the implications of our result for the description of angular momentum in quantum mechanics; in particular, we reexamine, in the light of this new evidence, the suggestion made by Einstein and Stern [Ann. Phys. 40, 551 (1913)] that there is a nontrivial distribution of angular momentum in the S state.