Wigner function for the orientation state

TL;DR

This paper introduces a Wigner function-based quantum phase space representation for the orientation states of extended objects, enabling intuitive analysis of quantum and semiclassical rotational phenomena.

Contribution

It presents a novel Wigner function for orientation states using Euler angles, extending phase space methods to rotational quantum systems.

Findings

Validates the approach with molecular alignment examples

Provides a phase space framework similar to standard Wigner functions

Enables intuitive discussion of quantum effects in rotation

Abstract

We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner function and thus provides an intuitive framework for discussing quantum effects and semiclassical approximations in the rotational motion. Examples illustrating the viability of this quasi-probability distribution include the phase space description of a molecular alignment effect.