Table of Clebsch–Gordan coefficients

This is a table of Clebsch–Gordan coefficients used for adding angular momentum values in quantum mechanics. The overall sign of the coefficients for each set of constant $j_1$ , $j_2$ , $j$ is arbitrary to some degree and has been fixed according to the Condon-Shortley and Wigner sign convention as discussed by Baird and Biedenharn.^[1] Tables with the same sign convention may be found in the Particle Data Group's Review of Particle Properties^[2] and in online tables.^[3]

Formulation

The Clebsch–Gordan coefficients are the solutions to

|(j_1j_2)jm\rangle = \sum_{m_1=-j_1}^{j_1} \sum_{m_2=-j_2}^{j_2} |j_1m_1j_2m_2\rangle \langle j_1j_2;m_1m_2|j_1j_2;jm\rangle

Explicitly:

\begin{align} \langle j_1j_2;m_1m_2|j_1j_2;jm\rangle = \ &\delta_{m,m_1+m_2} \sqrt{\frac{(2j+1)(j+j_1-j_2)!(j-j_1+j_2)!(j_1+j_2-j)!}{(j_1+j_2+j+1)!}}\ \times \\ &\sqrt{(j+m)!(j-m)!(j_1-m_1)!(j_1+m_1)!(j_2-m_2)!(j_2+m_2)!}\ \times \\ &\sum_k \frac{(-1)^k}{k!(j_1+j_2-j-k)!(j_1-m_1-k)!(j_2+m_2-k)!(j-j_2+m_1+k)!(j-j_1-m_2+k)!}. \end{align}

The summation is extended over all integer $k$ for which the argument of every factorial is nonnegative.^[4]

For brevity, solutions with $m < 0$ and $j 1 < j 2$ are omitted. They may be calculated using the simple relations

\langle j_1j_2;m_1m_2|j_1j_2;jm\rangle=(-1)^{j-j_1-j_2}\langle j_1j_2;-m_1,-m_2|j_1j_2;j,-m\rangle

and

\langle j_1j_2;m_1m_2|j_1j_2;jm\rangle=(-1)^{j-j_1-j_2} \langle j_2j_1;m_2m_1|j_2j_1;jm\rangle

A complete list ^[5]

$j 2 =0$

When $j 2 = 0$ , the Clebsch–Gordan coefficients are given by $\delta_{j,j_1}\delta_{m,m_1}$ .

$j 1 = 1 / 2, j 2 = 1 / 2$

$m =1$
$j$ $m 1, m 2$	1
1/2, 1/2	$1$

$m =-1$
$j$ $m 1, m 2$	1
-1/2, -1/2	$1$

$m =0$
$j$ $m 1, m 2$	1	0
1/2, -1/2	${\sqrt {\frac {1}{2}}}$	${\sqrt {\frac {1}{2}}}$
-1/2, 1/2	${\sqrt {\frac {1}{2}}}$	$-{\sqrt {\frac {1}{2}}}$

$j 1 =1, j 2 = 1 / 2$

$m = 3 / 2$
$j$ $m 1, m 2$	3/2
1, 1/2	$1$

$m = 1 / 2$
$j$ $m 1, m 2$	3/2	1/2
1, -1/2	${\sqrt {\frac {1}{3}}}$	${\sqrt {\frac {2}{3}}}$
0, 1/2	${\sqrt {\frac {2}{3}}}$	$-{\sqrt {\frac {1}{3}}}$

$j 1 =1, j 2 =1$

$m =2$
$j$ $m 1, m 2$	2
1, 1	$1$

$m =1$
$j$ $m 1, m 2$	2	1
1, 0	${\sqrt {\frac {1}{2}}}$	${\sqrt {\frac {1}{2}}}$
0, 1	${\sqrt {\frac {1}{2}}}$	$-{\sqrt {\frac {1}{2}}}$

$m =0$
$j$ $m 1, m 2$	2	1	0
1, -1	${\sqrt {\frac {1}{6}}}$	${\sqrt {\frac {1}{2}}}$	${\sqrt {\frac {1}{3}}}$
0, 0	${\sqrt {\frac {2}{3}}}$	$0$	$-{\sqrt {\frac {1}{3}}}$
-1, 1	${\sqrt {\frac {1}{6}}}$	$-{\sqrt {\frac {1}{2}}}$	${\sqrt {\frac {1}{3}}}$

$j 1 = 3 / 2, j 2 = 1 / 2$

$m =2$
$j$ $m 1, m 2$	2
3/2, 1/2	$1$

$m =1$
$j$ $m 1, m 2$	2	1
3/2, -1/2	${\frac {1}{2}}$	${\sqrt {\frac {3}{4}}}$
1/2, 1/2	${\sqrt {\frac {3}{4}}}$	$-{\frac {1}{2}}$

$m =0$
$j$ $m 1, m 2$	2	1
1/2, -1/2	${\sqrt {\frac {1}{2}}}$	${\sqrt {\frac {1}{2}}}$
-1/2, 1/2	${\sqrt {\frac {1}{2}}}$	$-{\sqrt {\frac {1}{2}}}$

$j 1 = 3 / 2, j 2 =1$

$m = 5 / 2$
$j$ $m 1, m 2$	5/2
3/2, 1	$1$

$m = 3 / 2$
$j$ $m 1, m 2$	5/2	3/2
3/2, 0	${\sqrt {\frac {2}{5}}}$	${\sqrt {\frac {3}{5}}}$
1/2, 1	${\sqrt {\frac {3}{5}}}$	$-{\sqrt {\frac {2}{5}}}$

$m = 1 / 2$
$j$ $m 1, m 2$	5/2	3/2	1/2
3/2, -1	${\sqrt {\frac {1}{10}}}$	${\sqrt {\frac {2}{5}}}$	${\sqrt {\frac {1}{2}}}$
1/2, 0	${\sqrt {\frac {3}{5}}}$	${\sqrt {\frac {1}{15}}}$	$-{\sqrt {\frac {1}{3}}}$
-1/2, 1	${\sqrt {\frac {3}{10}}}$	$-{\sqrt {\frac {8}{15}}}$	${\sqrt {\frac {1}{6}}}$

$j 1 = 3 / 2, j 2 = 3 / 2$

$m =3$
$j$ $m 1, m 2$	3
3/2, 3/2	$1$

$m =2$
$j$ $m 1, m 2$	3	2
3/2, 1/2	${\sqrt {\frac {1}{2}}}$	${\sqrt {\frac {1}{2}}}$
1/2, 3/2	${\sqrt {\frac {1}{2}}}$	$-{\sqrt {\frac {1}{2}}}$

$m =1$
$j$ $m 1, m 2$	3	2	1
3/2, -1/2	${\sqrt {\frac {1}{5}}}$	${\sqrt {\frac {1}{2}}}$	${\sqrt {\frac {3}{10}}}$
1/2, 1/2	${\sqrt {\frac {3}{5}}}$	$0$	$-{\sqrt {\frac {2}{5}}}$
-1/2, 3/2	${\sqrt {\frac {1}{5}}}$	$-{\sqrt {\frac {1}{2}}}$	${\sqrt {\frac {3}{10}}}$

$m =0$
$j$ $m 1, m 2$	3	2	1	0
3/2, -3/2	${\sqrt {\frac {1}{20}}}$	${\frac {1}{2}}$	${\sqrt {\frac {9}{20}}}$	${\frac {1}{2}}$
1/2, -1/2	${\sqrt {\frac {9}{20}}}$	${\frac {1}{2}}$	$-{\sqrt {\frac {1}{20}}}$	$-{\frac {1}{2}}$
-1/2, 1/2	${\sqrt {\frac {9}{20}}}$	$-{\frac {1}{2}}$	$-{\sqrt {\frac {1}{20}}}$	${\frac {1}{2}}$
-3/2, 3/2	${\sqrt {\frac {1}{20}}}$	$-{\frac {1}{2}}$	${\sqrt {\frac {9}{20}}}$	$-{\frac {1}{2}}$

$j 1 =2, j 2 = 1 / 2$

$m = 5 / 2$
$j$ $m 1, m 2$	5/2
2, 1/2	$1$

$m = 3 / 2$
$j$ $m 1, m 2$	5/2	3/2
2, -1/2	${\sqrt {\frac {1}{5}}}$	${\sqrt {\frac {4}{5}}}$
1, 1/2	${\sqrt {\frac {4}{5}}}$	$-{\sqrt {\frac {1}{5}}}$

$m = 1 / 2$
$j$ $m 1, m 2$	5/2	3/2
1, -1/2	${\sqrt {\frac {2}{5}}}$	${\sqrt {\frac {3}{5}}}$
0, 1/2	${\sqrt {\frac {3}{5}}}$	$-{\sqrt {\frac {2}{5}}}$

$j 1 =2, j 2 =1$

$m =3$
$j$ $m 1, m 2$	3
2, 1	$1$

$m =2$
$j$ $m 1, m 2$	3	2
2, 0	${\sqrt {\frac {1}{3}}}$	${\sqrt {\frac {2}{3}}}$
1, 1	${\sqrt {\frac {2}{3}}}$	$-{\sqrt {\frac {1}{3}}}$

$m =1$
$j$ $m 1, m 2$	3	2	1
2, -1	${\sqrt {\frac {1}{15}}}$	${\sqrt {\frac {1}{3}}}$	${\sqrt {\frac {3}{5}}}$
1, 0	${\sqrt {\frac {8}{15}}}$	${\sqrt {\frac {1}{6}}}$	$-{\sqrt {\frac {3}{10}}}$
0, 1	${\sqrt {\frac {2}{5}}}$	$-{\sqrt {\frac {1}{2}}}$	${\sqrt {\frac {1}{10}}}$

$m =0$
$j$ $m 1, m 2$	3	2	1
1, -1	${\sqrt {\frac {1}{5}}}$	${\sqrt {\frac {1}{2}}}$	${\sqrt {\frac {3}{10}}}$
0, 0	${\sqrt {\frac {3}{5}}}$	$0$	$-{\sqrt {\frac {2}{5}}}$
-1, 1	${\sqrt {\frac {1}{5}}}$	$-{\sqrt {\frac {1}{2}}}$	${\sqrt {\frac {3}{10}}}$

$j 1 =2, j 2 = 3 / 2$

$m = 7 / 2$
$j$ $m 1, m 2$	7/2
2, 3/2	$1$

$m = 5 / 2$
$j$ $m 1, m 2$	7/2	5/2
2, 1/2	${\sqrt {\frac {3}{7}}}$	${\sqrt {\frac {4}{7}}}$
1, 3/2	${\sqrt {\frac {4}{7}}}$	$-{\sqrt {\frac {3}{7}}}$

$m = 3 / 2$
$j$ $m 1, m 2$	7/2	5/2	3/2
2, -1/2	${\sqrt {\frac {1}{7}}}$	${\sqrt {\frac {16}{35}}}$	${\sqrt {\frac {2}{5}}}$
1, 1/2	${\sqrt {\frac {4}{7}}}$	${\sqrt {\frac {1}{35}}}$	$-{\sqrt {\frac {2}{5}}}$
0, 3/2	${\sqrt {\frac {2}{7}}}$	$-{\sqrt {\frac {18}{35}}}$	${\sqrt {\frac {1}{5}}}$

$m = 1 / 2$
$j$ $m 1, m 2$	7/2	5/2	3/2	1/2
2, -3/2	${\sqrt {\frac {1}{35}}}$	${\sqrt {\frac {6}{35}}}$	${\sqrt {\frac {2}{5}}}$	${\sqrt {\frac {2}{5}}}$
1, -1/2	${\sqrt {\frac {12}{35}}}$	${\sqrt {\frac {5}{14}}}$	$0$	$-{\sqrt {\frac {3}{10}}}$
0, 1/2	${\sqrt {\frac {18}{35}}}$	$-{\sqrt {\frac {3}{35}}}$	$-{\sqrt {\frac {1}{5}}}$	${\sqrt {\frac {1}{5}}}$
-1, 3/2	${\sqrt {\frac {4}{35}}}$	$-{\sqrt {\frac {27}{70}}}$	${\sqrt {\frac {2}{5}}}$	$-{\sqrt {\frac {1}{10}}}$

$j 1 =2, j 2 =2$

$m =4$
$j$ $m 1, m 2$	4
2, 2	$1$

$m =3$
$j$ $m 1, m 2$	4	3
2, 1	${\sqrt {\frac {1}{2}}}$	${\sqrt {\frac {1}{2}}}$
1, 2	${\sqrt {\frac {1}{2}}}$	$-{\sqrt {\frac {1}{2}}}$

$m =2$
$j$ $m 1, m 2$	4	3	2
2, 0	${\sqrt {\frac {3}{14}}}$	${\sqrt {\frac {1}{2}}}$	${\sqrt {\frac {2}{7}}}$
1, 1	${\sqrt {\frac {4}{7}}}$	$0$	$-{\sqrt {\frac {3}{7}}}$
0, 2	${\sqrt {\frac {3}{14}}}$	$-{\sqrt {\frac {1}{2}}}$	${\sqrt {\frac {2}{7}}}$

$m =1$
$j$ $m 1, m 2$	4	3	2	1
2, -1	${\sqrt {\frac {1}{14}}}$	${\sqrt {\frac {3}{10}}}$	${\sqrt {\frac {3}{7}}}$	${\sqrt {\frac {1}{5}}}$
1, 0	${\sqrt {\frac {3}{7}}}$	${\sqrt {\frac {1}{5}}}$	$-{\sqrt {\frac {1}{14}}}$	$-{\sqrt {\frac {3}{10}}}$
0, 1	${\sqrt {\frac {3}{7}}}$	$-{\sqrt {\frac {1}{5}}}$	$-{\sqrt {\frac {1}{14}}}$	${\sqrt {\frac {3}{10}}}$
-1, 2	${\sqrt {\frac {1}{14}}}$	$-{\sqrt {\frac {3}{10}}}$	${\sqrt {\frac {3}{7}}}$	$-{\sqrt {\frac {1}{5}}}$

$m =0$
$j$ $m 1, m 2$	4	3	2	1	0
2, -2	${\sqrt {\frac {1}{70}}}$	${\sqrt {\frac {1}{10}}}$	${\sqrt {\frac {2}{7}}}$	${\sqrt {\frac {2}{5}}}$	${\sqrt {\frac {1}{5}}}$
1, -1	${\sqrt {\frac {8}{35}}}$	${\sqrt {\frac {2}{5}}}$	${\sqrt {\frac {1}{14}}}$	$-{\sqrt {\frac {1}{10}}}$	$-{\sqrt {\frac {1}{5}}}$
0, 0	${\sqrt {\frac {18}{35}}}$	$0$	$-{\sqrt {\frac {2}{7}}}$	$0$	${\sqrt {\frac {1}{5}}}$
-1, 1	${\sqrt {\frac {8}{35}}}$	$-{\sqrt {\frac {2}{5}}}$	${\sqrt {\frac {1}{14}}}$	${\sqrt {\frac {1}{10}}}$	$-{\sqrt {\frac {1}{5}}}$
-2, 2	${\sqrt {\frac {1}{70}}}$	$-{\sqrt {\frac {1}{10}}}$	${\sqrt {\frac {2}{7}}}$	$-{\sqrt {\frac {2}{5}}}$	${\sqrt {\frac {1}{5}}}$

$j 1 = 5 / 2, j 2 = 1 / 2$

$m =3$
$j$ $m 1, m 2$	3
5/2, 1/2	$1$

$m =2$
$j$ $m 1, m 2$	3	2
5/2, -1/2	${\sqrt {\frac {1}{6}}}$	${\sqrt {\frac {5}{6}}}$
3/2, 1/2	${\sqrt {\frac {5}{6}}}$	$-{\sqrt {\frac {1}{6}}}$

$m =1$
$j$ $m 1, m 2$	3	2
3/2, -1/2	${\sqrt {\frac {1}{3}}}$	${\sqrt {\frac {2}{3}}}$
1/2, 1/2	${\sqrt {\frac {2}{3}}}$	$-{\sqrt {\frac {1}{3}}}$

$m =0$
$j$ $m 1, m 2$	3	2
1/2, -1/2	${\sqrt {\frac {1}{2}}}$	${\sqrt {\frac {1}{2}}}$
-1/2, 1/2	${\sqrt {\frac {1}{2}}}$	$-{\sqrt {\frac {1}{2}}}$

$j 1 = 5 / 2, j 2 =1$

$m = 7 / 2$
$j$ $m 1, m 2$	7/2
5/2, 1	$1$

$m = 5 / 2$
$j$ $m 1, m 2$	7/2	5/2
5/2, 0	${\sqrt {\frac {2}{7}}}$	${\sqrt {\frac {5}{7}}}$
3/2, 1	${\sqrt {\frac {5}{7}}}$	$-{\sqrt {\frac {2}{7}}}$

$m = 3 / 2$
$j$ $m 1, m 2$	7/2	5/2	3/2
5/2, -1	${\sqrt {\frac {1}{21}}}$	${\sqrt {\frac {2}{7}}}$	${\sqrt {\frac {2}{3}}}$
3/2, 0	${\sqrt {\frac {10}{21}}}$	${\sqrt {\frac {9}{35}}}$	$-{\sqrt {\frac {4}{15}}}$
1/2, 1	${\sqrt {\frac {10}{21}}}$	$-{\sqrt {\frac {16}{35}}}$	${\sqrt {\frac {1}{15}}}$

$m = 1 / 2$
$j$ $m 1, m 2$	7/2	5/2	3/2
3/2, -1	${\sqrt {\frac {1}{7}}}$	${\sqrt {\frac {16}{35}}}$	${\sqrt {\frac {2}{5}}}$
1/2, 0	${\sqrt {\frac {4}{7}}}$	${\sqrt {\frac {1}{35}}}$	$-{\sqrt {\frac {2}{5}}}$
-1/2, 1	${\sqrt {\frac {2}{7}}}$	$-{\sqrt {\frac {18}{35}}}$	${\sqrt {\frac {1}{5}}}$

$j 1 = 5 / 2, j 2 = 3 / 2$

$m =4$
$j$ $m 1, m 2$	4
5/2, 3/2	$1$

$m =3$
$j$ $m 1, m 2$	4	3
5/2, 1/2	${\sqrt {\frac {3}{8}}}$	${\sqrt {\frac {5}{8}}}$
3/2, 3/2	${\sqrt {\frac {5}{8}}}$	$-{\sqrt {\frac {3}{8}}}$

$m =2$
$j$ $m 1, m 2$	4	3	2
5/2, -1/2	${\sqrt {\frac {3}{28}}}$	${\sqrt {\frac {5}{12}}}$	${\sqrt {\frac {10}{21}}}$
3/2, 1/2	${\sqrt {\frac {15}{28}}}$	${\sqrt {\frac {1}{12}}}$	$-{\sqrt {\frac {8}{21}}}$
1/2, 3/2	${\sqrt {\frac {5}{14}}}$	$-{\sqrt {\frac {1}{2}}}$	${\sqrt {\frac {1}{7}}}$

$m =1$
$j$ $m 1, m 2$	4	3	2	1
5/2, -3/2	${\sqrt {\frac {1}{56}}}$	${\sqrt {\frac {1}{8}}}$	${\sqrt {\frac {5}{14}}}$	${\sqrt {\frac {1}{2}}}$
3/2, -1/2	${\sqrt {\frac {15}{56}}}$	${\sqrt {\frac {49}{120}}}$	${\sqrt {\frac {1}{42}}}$	$-{\sqrt {\frac {3}{10}}}$
1/2, 1/2	${\sqrt {\frac {15}{28}}}$	$-{\sqrt {\frac {1}{60}}}$	$-{\sqrt {\frac {25}{84}}}$	${\sqrt {\frac {3}{20}}}$
-1/2, 3/2	${\sqrt {\frac {5}{28}}}$	$-{\sqrt {\frac {9}{20}}}$	${\sqrt {\frac {9}{28}}}$	$-{\sqrt {\frac {1}{20}}}$

$m =0$
$j$ $m 1, m 2$	4	3	2	1
3/2, -3/2	${\sqrt {\frac {1}{14}}}$	${\sqrt {\frac {3}{10}}}$	${\sqrt {\frac {3}{7}}}$	${\sqrt {\frac {1}{5}}}$
1/2, -1/2	${\sqrt {\frac {3}{7}}}$	${\sqrt {\frac {1}{5}}}$	$-{\sqrt {\frac {1}{14}}}$	$-{\sqrt {\frac {3}{10}}}$
-1/2, 1/2	${\sqrt {\frac {3}{7}}}$	$-{\sqrt {\frac {1}{5}}}$	$-{\sqrt {\frac {1}{14}}}$	${\sqrt {\frac {3}{10}}}$
-3/2, 3/2	${\sqrt {\frac {1}{14}}}$	$-{\sqrt {\frac {3}{10}}}$	${\sqrt {\frac {3}{7}}}$	$-{\sqrt {\frac {1}{5}}}$

$j 1 = 5 / 2, j 2 =2$

$m = 9 / 2$
$j$ $m 1, m 2$	9/2
5/2, 2	$1$

$m = 7 / 2$
$j$ $m 1, m 2$	9/2	7/2
5/2, 1	${\frac {2}{3}}$	${\sqrt {\frac {5}{9}}}$
3/2, 2	${\sqrt {\frac {5}{9}}}$	$-{\frac {2}{3}}$

$m = 5 / 2$
$j$ $m 1, m 2$	9/2	7/2	5/2
5/2, 0	${\sqrt {\frac {1}{6}}}$	${\sqrt {\frac {10}{21}}}$	${\sqrt {\frac {5}{14}}}$
3/2, 1	${\sqrt {\frac {5}{9}}}$	${\sqrt {\frac {1}{63}}}$	$-{\sqrt {\frac {3}{7}}}$
1/2, 2	${\sqrt {\frac {5}{18}}}$	$-{\sqrt {\frac {32}{63}}}$	${\sqrt {\frac {3}{14}}}$

$m = 3 / 2$
$j$ $m 1, m 2$	9/2	7/2	5/2	3/2
5/2, -1	${\sqrt {\frac {1}{21}}}$	${\sqrt {\frac {5}{21}}}$	${\sqrt {\frac {3}{7}}}$	${\sqrt {\frac {2}{7}}}$
3/2, 0	${\sqrt {\frac {5}{14}}}$	${\sqrt {\frac {2}{7}}}$	$-{\sqrt {\frac {1}{70}}}$	$-{\sqrt {\frac {12}{35}}}$
1/2, 1	${\sqrt {\frac {10}{21}}}$	$-{\sqrt {\frac {2}{21}}}$	$-{\sqrt {\frac {6}{35}}}$	${\sqrt {\frac {9}{35}}}$
-1/2, 2	${\sqrt {\frac {5}{42}}}$	$-{\sqrt {\frac {8}{21}}}$	${\sqrt {\frac {27}{70}}}$	$-{\sqrt {\frac {4}{35}}}$

$m = 1 / 2$
$j$ $m 1, m 2$	9/2	7/2	5/2	3/2	1/2
5/2, -2	${\sqrt {\frac {1}{126}}}$	${\sqrt {\frac {4}{63}}}$	${\sqrt {\frac {3}{14}}}$	${\sqrt {\frac {8}{21}}}$	${\sqrt {\frac {1}{3}}}$
3/2, -1	${\sqrt {\frac {10}{63}}}$	${\sqrt {\frac {121}{315}}}$	${\sqrt {\frac {6}{35}}}$	$-{\sqrt {\frac {2}{105}}}$	$-{\sqrt {\frac {4}{15}}}$
1/2, 0	${\sqrt {\frac {10}{21}}}$	${\sqrt {\frac {4}{105}}}$	$-{\sqrt {\frac {8}{35}}}$	$-{\sqrt {\frac {2}{35}}}$	${\sqrt {\frac {1}{5}}}$
-1/2, 1	${\sqrt {\frac {20}{63}}}$	$-{\sqrt {\frac {14}{45}}}$	$0$	${\sqrt {\frac {5}{21}}}$	$-{\sqrt {\frac {2}{15}}}$
-3/2, 2	${\sqrt {\frac {5}{126}}}$	$-{\sqrt {\frac {64}{315}}}$	${\sqrt {\frac {27}{70}}}$	$-{\sqrt {\frac {32}{105}}}$	${\sqrt {\frac {1}{15}}}$

SU(N) Clebsch–Gordan coefficients

Algorithms to produce Clebsch–Gordan coefficients for higher values of $j_1$ and $j_2$ , or for the su(N) algebra instead of su(2), are known.^[6] A web interface for tabulating SU(N) Clebsch-Gordan coefficients is readily available.

References

↑ Baird, C.E.; L. C. Biedenharn (October 1964). "On the Representations of the Semisimple Lie Groups. III. The Explicit Conjugation Operation for SU_n". J. Math. Phys. 5: 1723–1730. Bibcode:1964JMP.....5.1723B. doi:10.1063/1.1704095.
↑ Hagiwara, K.; et al. (July 2002). "Review of Particle Properties" (PDF). Phys. Rev. D. 66: 010001. Bibcode:2002PhRvD..66a0001H. doi:10.1103/PhysRevD.66.010001. Retrieved 2007-12-20.
↑ Mathar, Richard J. (2006-08-14). "SO(3) Clebsch Gordan coefficients" (text). Retrieved 2012-10-15.
↑ (2.41), p. 172, Quantum Mechanics: Foundations and Applications, Arno Bohm, M. Loewe, New York: Springer-Verlag, 3rd ed., 1993, ISBN 0-387-95330-2.
↑ Weisbluth, Michael (1978). Atoms and molecules. ACADEMIC PRESS. p. 28. ISBN 0-12-744450-5. Table 1.4 resumes the most common.
↑ Alex, A.; M. Kalus; A. Huckleberry; J. von Delft (February 2011). "A numerical algorithm for the explicit calculation of SU(N) and SL(N,C) Clebsch-Gordan coefficients". J. Math. Phys. 82: 023507. Bibcode:2011JMP....52b3507A. arXiv:1009.0437 . doi:10.1063/1.3521562. Retrieved 2011-04-13.

External links

Online, Java-based Clebsch-Gordan Coefficient Calculator by Paul Stevenson
Other formulae for Clebsch–Gordan coefficients.
Web interface for tabulating SU(N) Clebsch-Gordan coefficients

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Table of Clebsch–Gordan coefficients

Formulation

A complete list [5]

j2=0

j1=1/2, j2=1/2

j1=1, j2=1/2

j1=1, j2=1

j1=3/2, j2=1/2

j1=3/2, j2=1

j1=3/2, j2=3/2

j1=2, j2=1/2

j1=2, j2=1

j1=2, j2=3/2

j1=2, j2=2

j1=5/2, j2=1/2

j1=5/2, j2=1

j1=5/2, j2=3/2

j1=5/2, j2=2