Vector coupling coefficients
Syntax: |
y = CLEBSG(j1,j2,j,m1,m2,m)
|
Clebsch-Gordan coefficients, Wigner's 3j, 6j, and 9j symbols, Jahn's U-function, and Racah coefficients are the vector coupling coefficients in the theory of angular momentum in quantum mechanics. For more information, please refer to:
Group Theory and its Application to the Quantum Mechanics of Atomic Spectra
by Eugene P. Wigner, Academic Press, 1959
Elementary Theory of Angular Momentum
by M.E. Rose, John Wiley & Sons, Inc., 1957
Angular Momentum in Quantum Mechanics
by A.R. Edmonds, Princeton University Press, 1960
The Clebsch-Gordan vector-addition coefficient,
is defined as:
and with the following restrictions:
Clebsch-Gordan coefficients
and
Wigner 3-j function
and
Wigner's 6-j function
Wigner's 9-j function
please refer to: Group Theory and its Application to the Quantum Mechanics of Atomic Spectra by Eugene P. Wigner, Academic Press, 1959
Racah coefficients
To define the Racah coefficients we first define the "triangle" coefficient:
Racah's W-function is defined as:
Jahn's U function