Coherent distributions for the rigid rotator

TL;DR

This paper introduces positive phase-space distributions for the classical rigid rotator that align with quantum mechanics, linking Liouville solutions to Wigner distributions and the Schrödinger equation.

Contribution

It presents a novel class of coherent solutions to the classical Liouville equation for the rigid rotator, connecting classical phase-space distributions with quantum quasiprobabilities.

Findings

Distributions are positive and associated with Hamilton-Jacobi theory.

Distributions become Wigner-type quasiprobabilities via discretization.

Expected Hamiltonian includes a finite zero-point energy.

Abstract

Coherent solutions of the classical Liouville equation for the rigid rotator are presented as positive phase-space distributions associated with the Lagrangian submanifolds of Hamilton-Jacobi theory. These solutions become Wigner-type quasiprobability distributions by a formal discretization of the left-invariant vector fields from their Fourier transform in angular momentum. The results are consistent with the usual quantization of the anisotropic rotator, but the expected value of the Hamiltonian contains a finite "zero point" energy term. It is shown that during the time when a quasiprobability distribution evolves according to the Liouville equation, the related quantum wave function should satisfy the time-dependent Schroedinger equation.