22
Wigner- and Clebsch-Gordan Coefficients
Abstract
Angular momenta and their coupling are a particular important concept for
quantum systems. The chapter target is the Clebsch-Gordan coefficients, Wigner
3j-, 6j-, and 9j-symbols. The evaluations are based on finite summations and the
quantum angular momentum coupling rules. The corresponding MATLAB code
can be downloaded.
Angular momenta and their coupling are a particular important concept for quantum
systems. The chapter target is the Clebsch-Gordan coefficients, Wigner 3j-, 6j-, and
9j-symbols.
Function Overview
The SPECFUNPHYS class
jjCG supports the evaluation of Clebsch-Gordan coefficients,
jj3j allows the evaluation of the Wigner 3j-symbol,
jj6j serves for the evaluation of the Wigner 6j-symbol, and
jj9j evaluates the Wigner 9j-symbol.
22.1 Fundamental Equations and Computation
22.1.1 Basic Aspects
The components of the angular momentum operator hold the following commutator
relations:
[ˆ r i , ˆ
L j ] = ij k i ¯
hˆ r k
(22.1a)
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
W. Schweizer, Special Functions in Physics with MATLAB,
https://doi.org/10.1007/978-3-030-64232-7_22
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