Tabla de coeficientes de Clebsch-Gordan

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Se utiliza para añadir valores de impulso angular en mecánica cuántica

Esto es un tabla de coeficientes Clebsch-Gordan utilizado para añadir valores de impulso angular en la mecánica cuántica. El signo general de los coeficientes para cada conjunto de constantes ${displaystyle j_{1}}$ , ${displaystyle j_{2}}$ , ${displaystyle j}$ es arbitraria en algún grado y se ha fijado de acuerdo con la convención de firmas Condon-Shortley y Wigner, como lo discutieron Baird y Biedenharn. Tablas con la misma convención de signos pueden encontrarse en el Grupo de Datos de partículas Valoración de las propiedades de partículas y en mesas en línea.

Formulación

Los coeficientes de Clebsch-Gordan son las soluciones a

{displaystyle |j_{1},j_{2};J,Mrangle =sum _{m_{1}=-j_{1}}^{j_{1}}sum _{m_{2}=-j_{2}}^{j_{2}}|j_{1},m_{1};j_{2},m_{2}rangle langle j_{1},j_{2};m_{1},m_{2}mid j_{1},j_{2};J,Mrangle }

Explícitamente:

{displaystyle {begin{aligned}&langle j_{1},j_{2};m_{1},m_{2}mid j_{1},j_{2};J,Mrangle \[6pt]={}&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 {}\[6pt]&{sqrt {(J+M)!(J-M)!(j_{1}-m_{1})!(j_{1}+m_{1})!(j_{2}-m_{2})!(j_{2}+m_{2})!}} times {}\[6pt]&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{aligned}}}

La suma se extiende a todos los enteros $k$ para los cuales el argumento de cada factorial no es negativo.

Para abreviar, las soluciones con $M < 0$ y $j 1 < j 2$ se omiten. Se pueden calcular usando las relaciones simples

{displaystyle langle j_{1},j_{2};m_{1},m_{2}mid j_{1},j_{2};J,Mrangle =(-1)^{J-j_{1}-j_{2}}langle j_{1},j_{2};-m_{1},-m_{2}mid j_{1},j_{2};J,-Mrangle.}

{displaystyle langle j_{1},j_{2};m_{1},m_{2}mid j_{1},j_{2};J,Mrangle =(-1)^{J-j_{1}-j_{2}}langle j_{2},j_{1};m_{2},m_{1}mid j_{2},j_{1};J,Mrangle.}

Valores específicos

A continuación se proporcionan los coeficientes de Clebsch-Gordan para valores j menores o iguales a 5/2.

j2 = 0

Cuando $j 2 = 0$ , los coeficientes Clebsch-Gordan son dados por ${displaystyle delta _{j,j_{1}}delta _{m,m_{1}}}$ .

j1 = 1/2, j2 = 1/2

$m = 2$
$j$ $m 1, m 2$	1
1/2, 1/2	${displaystyle 1}$

$m = 2$
$j$ $m 1, m 2$	1
−1/2, −1/2	${displaystyle 1}$

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

j1 = 1, j2 = 1/2

$m = {0}$
$j$ $m 1, m 2$	{0}
1, 1/2	${displaystyle 1}$

tamaño=100%m = {-1}
$j$ $m 1, m 2$	3/2	1/2
1, −1/2	${displaystyle {sqrt {frac {1}{3}}}}$	${displaystyle {sqrt {frac {2}{3}}}}$
0, 1/2	${displaystyle {sqrt {frac {2}{3}}}}$	${displaystyle -{sqrt {frac {1}{3}}}}$

j1 = 1, j2 = 1

$m = 2$
$j$ $m 1, m 2$	2
1, 1	${displaystyle 1}$

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

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

j1 = 3/2, j2 = 1/2

$m = 2$
$j$ $m 1, m 2$	2
3/2, 1/2	${displaystyle 1}$

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

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

j1 = 3/2, j2 = 1

$m = 5 / 2$
$j$ $m 1, m 2$	5/2
3/2, 1	${displaystyle 1}$

$m = 3 / 2$
$j$ $m 1, m 2$	5/2	3/2
3/20	${displaystyle {sqrt {frac {2}{5}}}}$	${displaystyle {sqrt {frac {3}{5}}}}$
1/2, 1	${displaystyle {sqrt {frac {3}{5}}}}$	${displaystyle -{sqrt {frac {2}{5}}}}$

$m = 1 / 2$
$j$ $m 1, m 2$	5/2	3/2	1/2
3/2, −1	${displaystyle {sqrt {frac {1}{10}}}}$	${displaystyle {sqrt {frac {2}{5}}}}$	${displaystyle {sqrt {frac {1}{2}}}}$
1/20	${displaystyle {sqrt {frac {3}{5}}}}$	${displaystyle {sqrt {frac {1}{15}}}}$	${displaystyle -{sqrt {frac {1}{3}}}}$
−1/2, 1	${displaystyle {sqrt {frac {3}{10}}}}$	${displaystyle -{sqrt {frac {8}{15}}}}$	${displaystyle {sqrt {frac {1}{6}}}}$

j1 = 3/2, j2 = 3/2

$m = 3$
$j$ $m 1, m 2$	3
3/2, 3/2	${displaystyle 1}$

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

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

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

j1 = 2, j2 = 1/2

$m = 5 / 2$
$j$ $m 1, m 2$	5/2
2, 1/2	${displaystyle 1}$

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

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

j1 = 2, j2 = 1

$m = 3$
$j$ $m 1, m 2$	3
2, 1	${displaystyle 1}$

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

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

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

j1 = 2, j2 = 3/2

$m = 7 / 2$
$j$ $m 1, m 2$	7/2
2, 3/2	${displaystyle 1}$

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

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

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

j1 = 2, j2 = 2

$m = 4$
$j$ $m 1, m 2$	4
2, 2	${displaystyle 1}$

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

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

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

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

j1 = 5/2, j2 = 1/2

$m = 3$
$j$ $m 1, m 2$	3
5/2, 1/2	${displaystyle 1}$

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

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

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

j1 = 5/2, j2 = 1

$m = 7 / 2$
$j$ $m 1, m 2$	7/2
5/2, 1	${displaystyle 1}$

$m = 5 / 2$
$j$ $m 1, m 2$	7/2	5/2
5/20	${displaystyle {sqrt {frac {2}{7}}}}$	${displaystyle {sqrt {frac {5}{7}}}}$
3/2, 1	${displaystyle {sqrt {frac {5}{7}}}}$	${displaystyle -{sqrt {frac {2}{7}}}}$

$m = 3 / 2$
$j$ $m 1, m 2$	7/2	5/2	3/2
5/2, −1	${displaystyle {sqrt {frac {1}{21}}}}$	${displaystyle {sqrt {frac {2}{7}}}}$	${displaystyle {sqrt {frac {2}{3}}}}$
3/20	${displaystyle {sqrt {frac {10}{21}}}}$	${displaystyle {sqrt {frac {9}{35}}}}$	${displaystyle -{sqrt {frac {4}{15}}}}$
1/2, 1	${displaystyle {sqrt {frac {10}{21}}}}$	${displaystyle -{sqrt {frac {16}{35}}}}$	${displaystyle {sqrt {frac {1}{15}}}}$

$m = 1 / 2$
$j$ $m 1, m 2$	7/2	5/2	3/2
3/2, −1	${displaystyle {sqrt {frac {1}{7}}}}$	${displaystyle {sqrt {frac {16}{35}}}}$	${displaystyle {sqrt {frac {2}{5}}}}$
1/20	${displaystyle {sqrt {frac {4}{7}}}}$	${displaystyle {sqrt {frac {1}{35}}}}$	${displaystyle -{sqrt {frac {2}{5}}}}$
−1/2, 1	${displaystyle {sqrt {frac {2}{7}}}}$	${displaystyle -{sqrt {frac {18}{35}}}}$	${displaystyle {sqrt {frac {1}{5}}}}$

j1 = 5/2, j2 = 3/2

$m = 4$
$j$ $m 1, m 2$	4
5/2, 3/2	${displaystyle 1}$

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

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

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

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

j1 = 5/2, j2 = 2

$m = 9 / 2$
$j$ $m 1, m 2$	9/2
5/2, 2	${displaystyle 1}$

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

$m = 5 / 2$
$j$ $m 1, m 2$	9/2	7/2	5/2
5/20	${displaystyle {sqrt {frac {1}{6}}}}$	${displaystyle {sqrt {frac {10}{21}}}}$	${displaystyle {sqrt {frac {5}{14}}}}$
3/2, 1	${displaystyle {sqrt {frac {5}{9}}}}$	${displaystyle {sqrt {frac {1}{63}}}}$	${displaystyle -{sqrt {frac {3}{7}}}}$
1/2, 2	${displaystyle {sqrt {frac {5}{18}}}}$	${displaystyle -{sqrt {frac {32}{63}}}}$	${displaystyle {sqrt {frac {3}{14}}}}$

$m = 3 / 2$
$j$ $m 1, m 2$	9/2	7/2	5/2	3/2
5/2, −1	${displaystyle {sqrt {frac {1}{21}}}}$	${displaystyle {sqrt {frac {5}{21}}}}$	${displaystyle {sqrt {frac {3}{7}}}}$	${displaystyle {sqrt {frac {2}{7}}}}$
3/20	${displaystyle {sqrt {frac {5}{14}}}}$	${displaystyle {sqrt {frac {2}{7}}}}$	${displaystyle -{sqrt {frac {1}{70}}}}$	${displaystyle -{sqrt {frac {12}{35}}}}$
1/2, 1	${displaystyle {sqrt {frac {10}{21}}}}$	${displaystyle -{sqrt {frac {2}{21}}}}$	${displaystyle -{sqrt {frac {6}{35}}}}$	${displaystyle {sqrt {frac {9}{35}}}}$
−1/2, 2	${displaystyle {sqrt {frac {5}{42}}}}$	${displaystyle -{sqrt {frac {8}{21}}}}$	${displaystyle {sqrt {frac {27}{70}}}}$	${displaystyle -{sqrt {frac {4}{35}}}}$

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

j1 = 5/2, j2 = 5/2

$m = 5$
$j$ $m 1, m 2$	5
5/2, 5/2	${displaystyle 1}$

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

$m = 3$
$j$ $m 1, m 2$	5	4	3
5/2, 1/2	${displaystyle {sqrt {frac {2}{9}}}}$	${displaystyle {sqrt {frac {1}{2}}}}$	${displaystyle {sqrt {frac {5}{18}}}}$
3/2, 3/2	${displaystyle {sqrt {frac {5}{9}}}}$	${displaystyle 0}$	${displaystyle -{frac {2}{3}}}$
1/2, 5/2	${displaystyle {sqrt {frac {2}{9}}}}$	${displaystyle -{sqrt {frac {1}{2}}}}$	${displaystyle {sqrt {frac {5}{18}}}}$

$m = 2$
$j$ $m 1, m 2$	5	4	3	2
5/2, −1/2	${displaystyle {sqrt {frac {1}{12}}}}$	${displaystyle {sqrt {frac {9}{28}}}}$	${displaystyle {sqrt {frac {5}{12}}}}$	${displaystyle {sqrt {frac {5}{28}}}}$
3/2, 1/2	${displaystyle {sqrt {frac {5}{12}}}}$	${displaystyle {sqrt {frac {5}{28}}}}$	${displaystyle -{sqrt {frac {1}{12}}}}$	${displaystyle -{sqrt {frac {9}{28}}}}$
1/2, 3/2	${displaystyle {sqrt {frac {5}{12}}}}$	${displaystyle -{sqrt {frac {5}{28}}}}$	${displaystyle -{sqrt {frac {1}{12}}}}$	${displaystyle {sqrt {frac {9}{28}}}}$
−1/2, 5/2	${displaystyle {sqrt {frac {1}{12}}}}$	${displaystyle -{sqrt {frac {9}{28}}}}$	${displaystyle {sqrt {frac {5}{12}}}}$	${displaystyle -{sqrt {frac {5}{28}}}}$

$m = 1$
$j$ $m 1, m 2$	5	4	3	2	1
5/2, −3/2	${displaystyle {sqrt {frac {1}{42}}}}$	${displaystyle {sqrt {frac {1}{7}}}}$	${displaystyle {sqrt {frac {1}{3}}}}$	${displaystyle {sqrt {frac {5}{14}}}}$	${displaystyle {sqrt {frac {1}{7}}}}$
3/2, −1/2	${displaystyle {sqrt {frac {5}{21}}}}$	${displaystyle {sqrt {frac {5}{14}}}}$	${displaystyle {sqrt {frac {1}{30}}}}$	${displaystyle -{sqrt {frac {1}{7}}}}$	${displaystyle -{sqrt {frac {8}{35}}}}$
1/2, 1/2	${displaystyle {sqrt {frac {10}{21}}}}$	${displaystyle 0}$	${displaystyle -{sqrt {frac {4}{15}}}}$	${displaystyle 0}$	${displaystyle {sqrt {frac {9}{35}}}}$
−1/2, 3/2	${displaystyle {sqrt {frac {5}{21}}}}$	${displaystyle -{sqrt {frac {5}{14}}}}$	${displaystyle {sqrt {frac {1}{30}}}}$	${displaystyle {sqrt {frac {1}{7}}}}$	${displaystyle -{sqrt {frac {8}{35}}}}$
−3/2, 5/2	${displaystyle {sqrt {frac {1}{42}}}}$	${displaystyle -{sqrt {frac {1}{7}}}}$	${displaystyle {sqrt {frac {1}{3}}}}$	${displaystyle -{sqrt {frac {5}{14}}}}$	${displaystyle {sqrt {frac {1}{7}}}}$

$m = 0$
$j$ $m 1, m 2$	5	4	3	2	1	0
5/2, −5/2	${displaystyle {sqrt {frac {1}{252}}}}$	${displaystyle {sqrt {frac {1}{28}}}}$	${displaystyle {sqrt {frac {5}{36}}}}$	${displaystyle {sqrt {frac {25}{84}}}}$	${displaystyle {sqrt {frac {5}{14}}}}$	${displaystyle {sqrt {frac {1}{6}}}}$
3/2, −3/2	${displaystyle {sqrt {frac {25}{252}}}}$	${displaystyle {sqrt {frac {9}{28}}}}$	${displaystyle {sqrt {frac {49}{180}}}}$	${displaystyle {sqrt {frac {1}{84}}}}$	${displaystyle -{sqrt {frac {9}{70}}}}$	${displaystyle -{sqrt {frac {1}{6}}}}$
1/2, −1/2	${displaystyle {sqrt {frac {25}{63}}}}$	${displaystyle {sqrt {frac {1}{7}}}}$	${displaystyle -{sqrt {frac {4}{45}}}}$	${displaystyle -{sqrt {frac {4}{21}}}}$	${displaystyle {sqrt {frac {1}{70}}}}$	${displaystyle {sqrt {frac {1}{6}}}}$
−1/2, 1/2	${displaystyle {sqrt {frac {25}{63}}}}$	${displaystyle -{sqrt {frac {1}{7}}}}$	${displaystyle -{sqrt {frac {4}{45}}}}$	${displaystyle {sqrt {frac {4}{21}}}}$	${displaystyle {sqrt {frac {1}{70}}}}$	${displaystyle -{sqrt {frac {1}{6}}}}$
−3/2, 3/2	${displaystyle {sqrt {frac {25}{252}}}}$	${displaystyle -{sqrt {frac {9}{28}}}}$	${displaystyle {sqrt {frac {49}{180}}}}$	${displaystyle -{sqrt {frac {1}{84}}}}$	${displaystyle -{sqrt {frac {9}{70}}}}$	${displaystyle {sqrt {frac {1}{6}}}}$
−5/2, 5/2	${displaystyle {sqrt {frac {1}{252}}}}$	${displaystyle -{sqrt {frac {1}{28}}}}$	${displaystyle {sqrt {frac {5}{36}}}}$	${displaystyle -{sqrt {frac {25}{84}}}}$	${displaystyle {sqrt {frac {5}{14}}}}$	${displaystyle -{sqrt {frac {1}{6}}}}$

SU(N) Coeficientes de Clebsch-Gordan

Algoritmos para producir coeficientes Clebsch–Gordan para valores superiores de ${displaystyle j_{1}}$ y ${displaystyle j_{2}}$ , o para el álgebra su(N) en lugar de su 2), son conocidos. Una interfaz web para tabular los coeficientes SU(N) Clebsch–Gordan está fácilmente disponible.

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