Quantum numbers and Angular Momentum Algebra

Testing properties of

$6j$ symbols

The above properties of

$6j$ symbols can again be tested using the symbolic python package wigner. Let us test the invariance

$\begin{Bmatrix} j_1 & j_2 & j_3\\ j_4 & j_5 & j_6 \end{Bmatrix} = \begin{Bmatrix} j_2 & j_1 & j_3\\ j_5 & j_4 & j_6 \end{Bmatrix}.$

The following program tests this relation for the case of $j_1=3/2$ , $j_2=3/2$ , $j_3=3$ , $j_4=1/2$ , $j_5=1/2$ , $j_6=1$

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from sympy import S
from sympy.physics.wigner import wigner_6j
# Twice the values of all js
j1 = 3
j2 = 5
j3 = 2
j4 = 3
j5 = 5
j6 = 1
""" The triangular relation has to be fulfilled """
print wigner_6j(S(j1)/2, S(j2)/2, j3, S(j4)/2, S(j5)/2, j6)
""" Swapping columns 1 <==> 2 """
print wigner_6j(S(j2)/2, S(j1)/2, j3, S(j5)/2, S(j4)/2, j6)

Testing properties of 6j 6j symbols

Testing properties of $6j$ symbols