Improved Recursive Computation of Clebsch-Gordan Coefficients

TL;DR

This paper introduces a sign-exponent recurrence method that enhances the stability and accuracy of recursive calculations of Clebsch-Gordan coefficients for large quantum numbers, benefiting various scientific applications.

Contribution

The paper presents a novel sign-exponent recurrence technique that improves the numerical stability of recursive C-G coefficient computations for large quantum numbers.

Findings

Significantly improved numerical stability.

Accurate computation for large quantum numbers.

Maintains efficiency of recursive methods.

Abstract

Fast, accurate, and stable computation of the Clebsch-Gordan (C-G) coefficients is always desirable, for example, in light scattering simulations, the translation of the multipole fields, quantum physics and chemistry. Current recursive methods for computing the C-G coefficients are often unstable for large quantum numbers due to numerical overflow or underflow. In this paper, we present an improved method, the so-called sign-exponent recurrence, for the recursive computation of C-G coefficients. The result shows that the proposed method can significantly improve the stability of the computation without losing its efficiency, producing accurate values for the C-G coefficients even with very large quantum numbers.