Vector coupling coefficients

Syntax: | `y = CLEBSG(j1,j2,j,m1,m2,m) y = WIGN3J(j1,j1,j,m1,m2,m) y = WIGN6J(j1,j2.j,m1,m2,m) y = WIGN9J(j1,j2,j,m1,m2,m,n1,n2,n) y = RACAH(a,b,c,d,e,f) y = JAHNUF(j1,j2,m2,m1,j,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