# On Quantum States for angular Position and Angular Momentum of Light

Source: [On Quantum States for angular Position and Angular Momentum of Light](<https://www.sota2.com/research/paper/68fa45fa1e209131ce91cdd4>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T05:34:54.642Z

Authors: Bo-Sture K. Skagerstam, Per K. Rekdal

Published: 2023-12-27T11:31:59.000Z

## Abstract

In the present paper we construct a properly defined quantum state expressed in terms of elliptic Jacobi theta functions for the self-adjoint observables angular position $\\theta$ and the corresponding angular momentum operator $L = -id/d\\theta$. The quantum uncertainties $\\Delta \\theta$ and $\\Delta L$ for the state are well-defined and are, e.g., shown to give a lower value of the uncertainty product $\\Delta \\theta \\Delta L$ than the minimal uncertainty states of Ref.\\cite{Padgett\_2004}. The mean value $\< L \>$ of the state is not required to be an integer. In the case of any half-integer mean value $\< L \>$ the state constructed exhibits a remarkable critical behavior with upper and lower bounds $\\Delta \\theta \< \\sqrt{\\pi^2/3 -2}$ and $\\Delta L \> 1/2$.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2312.16535>)

[PDF](<https://arxiv.org/pdf/2312.16535.pdf>)