Analytical formula for numerical evaluations of the Wigner rotation matrices at high spins

TL;DR

This paper introduces an analytical Fourier series approach to accurately compute Wigner d functions at high spins, overcoming numerical errors inherent in traditional polynomial methods.

Contribution

It presents a novel Fourier series representation of Wigner d functions and provides precise coefficient tables to improve high-spin numerical evaluations.

Findings

Fourier series representation reduces numerical errors at high spins.

Web-based tables enable accurate computation of Wigner d functions.

Method improves reliability of quantum angular momentum calculations.

Abstract

The Wigner d function, which is the essential part of an irreducible representation of SU(2) and SO(3) parameterized with Euler angles, has been know to suffer from a serious numerical errors at high spins, if it is calculated by means of the Wigner formula as a polynomial of cos and sin of half of the second Euler angle. This paper shows a way to avoid this problem by expressing the d functions as the Fourier series of the half angle. A precise numerical table of the coefficients of the series is obtainable from a web site.