Improved recursive computation of clebsch-Gordan coefficients
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, called the 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.
- Publication:
-
Journal of Quantitative Spectroscopy and Radiative Transfer
- Pub Date:
- October 2020
- DOI:
- 10.1016/j.jqsrt.2020.107210
- arXiv:
- arXiv:2006.04267
- Bibcode:
- 2020JQSRT.25407210X
- Keywords:
-
- Clebsch-Gordan coefficients;
- Recursive computation;
- Light scattering;
- Translation coefficients;
- Multipole fields;
- T-Matrix;
- Physics - Computational Physics;
- Physics - Optics;
- Quantum Physics
- E-Print:
- 15 pages, 3 figure, 1 table