Quantum States Allowing Minimum Uncertainty Product of angular position and momentum

TL;DR

This paper establishes the precise conditions under which quantum states can achieve an arbitrarily small uncertainty product between angular position and momentum, with illustrative examples demonstrating these conditions.

Contribution

It provides necessary and sufficient criteria for states to have minimal uncertainty products in angular variables, advancing understanding of quantum uncertainty relations.

Findings

Identified conditions for arbitrarily small uncertainty products

Provided analytical examples illustrating these conditions

Enhanced theoretical understanding of angular uncertainty in quantum states

Abstract

We provide necessary and sufficient conditions for states to have an arbitrarily small uncertainty product of the azimuthal angle $\phi $ and its canonical moment $L_{z}$. We illustrate our results with analytical examples.