Anexo:Tabla de coeficientes de Clebsch-Gordan

Esta es una tabla de coeficientes de Clebsch-Gordan usada para sumar momentos angulares en mecánica cuántica. El signo global de los coeficientes para cada conjunto de ${\displaystyle j_{1}}$, ${\displaystyle j_{2}}$ y ${\displaystyle j}$ constantes es en cierto grado arbitrario y ha sido fijado de acuerdo con la convención de Condon-Shortley y Wigner como viene dada en Baird and Biedenharn .^[1] Tablas con la misma convención de signos pueden ser encontradas en Review of Particle Properties ^[2] del Particle Data Group y en tablas en línea.^[3]

Para ver su formulación y definición formal vea coeficientes Clebsch—Gordan.

Formulación

Los estados de momento angular total pueden ser expandidos usando la relación de completitud en las bases de momentos angulares parciales como

${\displaystyle |(j_{1}j_{2})JM\rangle =\sum _{m_{1}=-j_{1}}^{j_{1}}\sum _{m_{2}=-j_{2}}^{j_{2}}|j_{1}m_{1}j_{2}m_{2}\rangle \langle j_{1}m_{1}j_{2}m_{2}|JM\rangle =\sum _{m_{1}=-j_{1}}^{j_{1}}\sum _{m_{2}=-j_{2}}^{j_{2}}|j_{1}m_{1}\rangle |j_{2}m_{2}\rangle \langle j_{1}m_{1}j_{2}m_{2}|JM\rangle }$

Los coeficientes ${\displaystyle \langle j_{1}m_{1}j_{2}m_{2}|JM\rangle }$ de la expansión son los coeficientes de Clebsch–Gordan. Estos se pueden escribir explícitamente como

${\displaystyle \langle j_{1}m_{1}j_{2}m_{2}|jm\rangle =\delta _{m,m_{1}+m_{2}}{\sqrt {\frac {(2j+1)(j+j_{1}-j_{2})!(j-j_{1}+j_{2})!(j_{1}+j_{2}-j)!}{(j_{1}+j_{2}+j+1)!}}}\ \times }$

${\displaystyle {\sqrt {(j+m)!(j-m)!(j_{1}-m_{1})!(j_{1}+m_{1})!(j_{2}-m_{2})!(j_{2}+m_{2})!}}\ \times }$

${\displaystyle \sum _{k}{\frac {(-1)^{k}}{k!(j_{1}+j_{2}-j-k)!(j_{1}-m_{1}-k)!(j_{2}+m_{2}-k)!(j-j_{2}+m_{1}+k)!(j-j_{1}-m_{2}+k)!}}.}$

Donde la suma se hace sobre todos los k enteros para los para los que los argumentos de todos los factoriales involucrados sean no negativos.^[4] Por brevedad, las soluciones con ${\displaystyle m<0}$ son omitidas, pero pueden ser calculadas usando la siguiente relación

${\displaystyle \langle j_{1},m_{1},j_{2},m_{2}|j,m\rangle =(-1)^{j-j_{1}-j_{2}}\langle j_{1},-m_{1},j_{2},-m_{2}|j,-m\rangle }$ .

j1=1/2, j2=1/2

m=1	j=
m1, m2=	1 1/2, 1/2 ${\displaystyle 1\!\,}$

m=0	j=
m1, m2=	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=3/2	j=
m1, m2=	3/2 1, 1/2 ${\displaystyle 1\!\,}$

m=1/2	j=
m1, m2=	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=
m1, m2=	2 1, 1 ${\displaystyle 1\!\,}$

m=1	j=
m1, m2=	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=

m1, m2=

2 1 0 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=
m1, m2=	2 3/2, 1/2 ${\displaystyle 1\!\,}$

m=1	j=
m1, m2=	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=
m1, m2=	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=
m1, m2=	5/2 3/2, 1 ${\displaystyle 1\!\,}$

m=3/2	j=
m1, m2=	5/2 3/2 3/2, 0 ${\displaystyle {\sqrt {\frac {2}{5}}}\!\,}$ ${\displaystyle {\sqrt {\frac {3}{5}}}\!\,}$ 1/2, 1 ${\displaystyle {\sqrt {\frac {3}{5}}}\!\,}$ ${\displaystyle -{\sqrt {\frac {2}{5}}}\!\,}$

m=1/2

j=

m1, m2=

5/2 3/2 1/2 3/2, -1 ${\displaystyle {\sqrt {\frac {1}{10}}}\!\,}$ ${\displaystyle {\sqrt {\frac {2}{5}}}\!\,}$ ${\displaystyle {\sqrt {\frac {1}{2}}}\!\,}$ 1/2, 0 ${\displaystyle {\sqrt {\frac {3}{5}}}\!\,}$ ${\displaystyle {\sqrt {\frac {1}{15}}}\!\,}$ ${\displaystyle -{\sqrt {\frac {1}{3}}}\!\,}$ -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=
m1, m2=	3 3/2, 3/2 ${\displaystyle 1\!\,}$

m=2	j=
m1, m2=	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=

m1, m2=

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=

m1, m2=

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=
m1, m2=	5/2 2, 1/2 ${\displaystyle 1\!\,}$

m=3/2	j=
m1, m2=	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=
m1, m2=	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=
m1, m2=	3 2, 1 ${\displaystyle 1\!\,}$

m=2	j=
m1, m2=	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=

m1, m2=

3 2 1 2, -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=

m1, m2=

3 2 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=
m1, m2=	7/2 2, 3/2 ${\displaystyle 1\!\,}$

m=5/2	j=
m1, m2=	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=

m1, m2=

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=

m1, m2=

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=
m1, m2=	4 2, 2 ${\displaystyle 1\!\,}$

m=3	j=
m1, m2=	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=

m1, m2=

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=

m1, m2=

4 3 2 1 2, -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=

m1, m2=

4 3 2 1 0 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 ${\displaystyle {\sqrt {\frac {8}{35}}}\!\,}$ ${\displaystyle {\sqrt {\frac {2}{5}}}\!\,}$ ${\displaystyle {\sqrt {\frac {1}{14}}}\!\,}$ ${\displaystyle -{\sqrt {\frac {1}{10}}}\!\,}$ ${\displaystyle -{\sqrt {\frac {1}{5}}}\!\,}$ 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=
m1, m2=	3 5/2, 1/2 ${\displaystyle 1\!\,}$

m=2	j=
m1, m2=	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=
m1, m2=	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=
m1, m2=	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=
m1, m2=	7/2 5/2, 1 ${\displaystyle 1\!\,}$

m=5/2	j=
m1, m2=	7/2 5/2 5/2, 0 ${\displaystyle {\sqrt {\frac {2}{7}}}\!\,}$ ${\displaystyle {\sqrt {\frac {5}{7}}}\!\,}$ 3/2, 1 ${\displaystyle {\sqrt {\frac {5}{7}}}\!\,}$ ${\displaystyle -{\sqrt {\frac {2}{7}}}\!\,}$

m=3/2

j=

m1, m2=

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

m=1/2

j=

m1, m2=

7/2 5/2 3/2 3/2, -1 ${\displaystyle {\sqrt {\frac {1}{7}}}\!\,}$ ${\displaystyle {\sqrt {\frac {16}{35}}}\!\,}$ ${\displaystyle {\sqrt {\frac {2}{5}}}\!\,}$ 1/2, 0 ${\displaystyle {\sqrt {\frac {4}{7}}}\!\,}$ ${\displaystyle {\sqrt {\frac {1}{35}}}\!\,}$ ${\displaystyle -{\sqrt {\frac {2}{5}}}\!\,}$ -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=
m1, m2=	4 5/2, 3/2 ${\displaystyle 1\!\,}$

m=3	j=
m1, m2=	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=

m1, m2=

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=

m1, m2=

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=

m1, m2=

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=
m1, m2=	9/2 5/2, 2 ${\displaystyle 1\!\,}$

m=7/2	j=
m1, m2=	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=

m1, m2=

9/2 7/2 5/2 5/2, 0 ${\displaystyle {\sqrt {\frac {1}{6}}}\!\,}$ ${\displaystyle {\sqrt {\frac {10}{21}}}\!\,}$ ${\displaystyle {\sqrt {\frac {5}{14}}}\!\,}$ 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=

m1, m2=

9/2 7/2 5/2 3/2 5/2, -1 ${\displaystyle {\sqrt {\frac {1}{21}}}\!\,}$ ${\displaystyle {\sqrt {\frac {5}{21}}}\!\,}$ ${\displaystyle {\sqrt {\frac {3}{7}}}\!\,}$ ${\displaystyle {\sqrt {\frac {2}{7}}}\!\,}$ 3/2, 0 ${\displaystyle {\sqrt {\frac {5}{14}}}\!\,}$ ${\displaystyle {\sqrt {\frac {2}{7}}}\!\,}$ ${\displaystyle -{\sqrt {\frac {1}{70}}}\!\,}$ ${\displaystyle -{\sqrt {\frac {12}{35}}}\!\,}$ 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=

m1, m2=

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 ${\displaystyle {\sqrt {\frac {10}{63}}}\!\,}$ ${\displaystyle {\sqrt {\frac {121}{315}}}\!\,}$ ${\displaystyle {\sqrt {\frac {6}{35}}}\!\,}$ ${\displaystyle -{\sqrt {\frac {2}{105}}}\!\,}$ ${\displaystyle -{\sqrt {\frac {4}{15}}}\!\,}$ 1/2, 0 ${\displaystyle {\sqrt {\frac {10}{21}}}\!\,}$ ${\displaystyle {\sqrt {\frac {4}{105}}}\!\,}$ ${\displaystyle -{\sqrt {\frac {8}{35}}}\!\,}$ ${\displaystyle -{\sqrt {\frac {2}{35}}}\!\,}$ ${\displaystyle {\sqrt {\frac {1}{5}}}\!\,}$ -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 ${\displaystyle {\sqrt {\frac {5}{126}}}\!\,}$ ${\displaystyle -{\sqrt {\frac {64}{315}}}\!\,}$ ${\displaystyle {\sqrt {\frac {27}{70}}}\!\,}$ ${\displaystyle -{\sqrt {\frac {32}{105}}}\!\,}$ ${\displaystyle {\sqrt {\frac {1}{15}}}\!\,}$