2023/12/27 by Bo-Sture Skagerstam, Skagerstam, Bo-Sture K., Per Kristian Rekdal +1
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Optics (physics.optics) #Orbital Angular Momentum in Optics #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2312.16535
openalex publication_date 2023/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 θ and the corresponding angular momentum operator L = -id/dθ. The quantum uncertainties Δθ and ΔL for the state are well-defined and are, e.g., shown to give a lower value of the uncertainty product ΔθΔL than the minimal uncertainty states of Ref.\citePadgett2004. 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 Δθ< √(π2/3 -2) and ΔL > 1/2.