Coherent states for a particle on a sphere

TL;DR

This paper introduces coherent states for a particle on a sphere, linking quantum states to classical phase space points, and demonstrates their effectiveness through an example of a rotator.

Contribution

It extends the concept of coherent states to a particle on a sphere, providing a new framework for approximating classical phase space in quantum systems.

Findings

Coherent states are labeled by points in the classical phase space.

Expectation values in these states approximate classical variables.

The approach is validated with an example of a rotator.

Abstract

The coherent states for a particle on a sphere are introduced. These states are labelled by points of the classical phase space, that is the position on the sphere and the angular momentum of a particle. As with the coherent states for a particle on a circle discussed in Kowalski K {\em et al} 1996 {\em J. Phys. A} {\bf 29} 4149, we deal with a deformation of the classical phase space related with quantum fluctuations. The expectation values of the position and the angular momentum in the coherent states are regarded as the best possible approximation of the classical phase space. The correctness of the introduced coherent states is illustrated by an example of the rotator.