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]

1 Formulation
2 SU(N) Clebsch-Gordan coefficients
3 References
4 External links

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:

$\langle j_1j_2;m_1m_2|j_1j_2;jm\rangle=$

$\delta_{m,m_1%2Bm_2} \sqrt{\frac{(2j%2B1)(j%2Bj_1-j_2)!(j-j_1%2Bj_2)!(j_1%2Bj_2-j)! }{(j_1%2Bj_2%2Bj%2B1)!}} \ \times$

$\sqrt{(j%2Bm)!(j-m)!(j_1-m_1)!(j_1%2Bm_1)!(j_2-m_2)!(j_2%2Bm_2)!}\ \times$

$\sum_k \frac{(-1)^k}{k!(j_1%2Bj_2-j-k)!(j_1-m_1-k)!(j_2%2Bm_2-k)!(j-j_2%2Bm_1%2Bk)!(j-j_1-m_2%2Bk)!}.$

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

For brevity, solutions with m < 0 and j₁ < j₂ 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

$\langle j_1j_2;m_1m_2|j_1j_2;jm\rangle=(-1)^{j_1%2Bj_2-J} \langle j_2 m_2 j_1 m_1|j_1j_2;jm\rangle$ .

j₂=0

When j₂ = 0, the Clebsch-Gordan coefficients are given by $\delta_{j,j_1}\delta_{m,m_1}$ .

j₁=1/2, j₂=1/2

m=1

m₁, m₂=

	1
1/2, 1/2	$1\!\,$

m=0

m₁, m₂=

	1	0
1/2, -1/2	$\sqrt{\frac{1}{2}}\!\,$	$\sqrt{\frac{1}{2}}\!\,$
-1/2, 1/2	$\sqrt{\frac{1}{2}}\!\,$	$-\sqrt{\frac{1}{2}}\!\,$

j₁=1, j₂=1/2

m=3/2

m₁, m₂=

	3/2
1, 1/2	$1\!\,$

m=1/2

m₁, m₂=

	3/2	1/2
1, -1/2	$\sqrt{\frac{1}{3}}\!\,$	$\sqrt{\frac{2}{3}}\!\,$
0, 1/2	$\sqrt{\frac{2}{3}}\!\,$	$-\sqrt{\frac{1}{3}}\!\,$

j₁=1, j₂=1

m=2

m₁, m₂=

	2
1, 1	$1\!\,$

m=1

m₁, m₂=

	2	1
1, 0	$\sqrt{\frac{1}{2}}\!\,$	$\sqrt{\frac{1}{2}}\!\,$
0, 1	$\sqrt{\frac{1}{2}}\!\,$	$-\sqrt{\frac{1}{2}}\!\,$

m=0

m₁, m₂=

	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	$\sqrt{\frac{1}{6}}\!\,$	$-\sqrt{\frac{1}{2}}\!\,$	$\sqrt{\frac{1}{3}}\!\,$

j₁=3/2, j₂=1/2

m=2

m₁, m₂=

	2
3/2, 1/2	$1\!\,$

m=1

m₁, m₂=

	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

m₁, m₂=

	2	1
1/2, -1/2	$\sqrt{\frac{1}{2}}\!\,$	$\sqrt{\frac{1}{2}}\!\,$
-1/2, 1/2	$\sqrt{\frac{1}{2}}\!\,$	$-\sqrt{\frac{1}{2}}\!\,$

j₁=3/2, j₂=1

m=5/2

m₁, m₂=

	5/2
3/2, 1	$1\!\,$

m=3/2

m₁, m₂=

	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

m₁, m₂=

	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	$\sqrt{\frac{3}{10}}\!\,$	$-\sqrt{\frac{8}{15}}\!\,$	$\sqrt{\frac{1}{6}}\!\,$

j₁=3/2, j₂=3/2

m=3

m₁, m₂=

	3
3/2, 3/2	$1\!\,$

m=2

m₁, m₂=

	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

m₁, m₂=

	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

m₁, m₂=

	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	$\sqrt{\frac{1}{20}}\!\,$	$-\frac{1}{2}\!\,$	$\sqrt{\frac{9}{20}}\!\,$	$-\frac{1}{2}\!\,$

j₁=2, j₂=1/2

m=5/2

m₁, m₂=

	5/2
2, 1/2	$1\!\,$

m=3/2

m₁, m₂=

	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

m₁, m₂=

	5/2	3/2
1, -1/2	$\sqrt{\frac{2}{5}}\!\,$	$\sqrt{\frac{3}{5}}\!\,$
0, 1/2	$\sqrt{\frac{3}{5}}\!\,$	$-\sqrt{\frac{2}{5}}\!\,$

j₁=2, j₂=1

m=3

m₁, m₂=

	3
2, 1	$1\!\,$

m=2

m₁, m₂=

	3	2
2, 0	$\sqrt{\frac{1}{3}}\!\,$	$\sqrt{\frac{2}{3}}\!\,$
1, 1	$\sqrt{\frac{2}{3}}\!\,$	$-\sqrt{\frac{1}{3}}\!\,$

m=1

m₁, m₂=

	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

m₁, m₂=

	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	$\sqrt{\frac{1}{5}}\!\,$	$-\sqrt{\frac{1}{2}}\!\,$	$\sqrt{\frac{3}{10}}\!\,$

j₁=2, j₂=3/2

m=7/2

m₁, m₂=

	7/2
2, 3/2	$1\!\,$

m=5/2

m₁, m₂=

	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

m₁, m₂=

	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

m₁, m₂=

	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	$\sqrt{\frac{4}{35}}\!\,$	$-\sqrt{\frac{27}{70}}\!\,$	$\sqrt{\frac{2}{5}}\!\,$	$-\sqrt{\frac{1}{10}}\!\,$

j₁=2, j₂=2

m=4

m₁, m₂=

	4
2, 2	$1\!\,$

m=3

m₁, m₂=

	4	3
2, 1	$\sqrt{\frac{1}{2}}\!\,$	$\sqrt{\frac{1}{2}}\!\,$
1, 2	$\sqrt{\frac{1}{2}}\!\,$	$-\sqrt{\frac{1}{2}}\!\,$

m=2

m₁, m₂=

	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

m₁, m₂=

	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

m₁, m₂=

	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	$\sqrt{\frac{1}{70}}\!\,$	$-\sqrt{\frac{1}{10}}\!\,$	$\sqrt{\frac{2}{7}}\!\,$	$-\sqrt{\frac{2}{5}}\!\,$	$\sqrt{\frac{1}{5}}\!\,$

j₁=5/2, j₂=1/2

m=3

m₁, m₂=

	3
5/2, 1/2	$1\!\,$

m=2

m₁, m₂=

	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

m₁, m₂=

	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

m₁, m₂=

	3	2
1/2, -1/2	$\sqrt{\frac{1}{2}}\!\,$	$\sqrt{\frac{1}{2}}\!\,$
-1/2, 1/2	$\sqrt{\frac{1}{2}}\!\,$	$-\sqrt{\frac{1}{2}}\!\,$

j₁=5/2, j₂=1

m=7/2

m₁, m₂=

	7/2
5/2, 1	$1\!\,$

m=5/2

m₁, m₂=

	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

m₁, m₂=

	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

m₁, m₂=

	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	$\sqrt{\frac{2}{7}}\!\,$	$-\sqrt{\frac{18}{35}}\!\,$	$\sqrt{\frac{1}{5}}\!\,$

j₁=5/2, j₂=3/2

m=4

m₁, m₂=

	4
5/2, 3/2	$1\!\,$

m=3

m₁, m₂=

	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

m₁, m₂=

	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

m₁, m₂=

	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

m₁, m₂=

	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	$\sqrt{\frac{1}{14}}\!\,$	$-\sqrt{\frac{3}{10}}\!\,$	$\sqrt{\frac{3}{7}}\!\,$	$-\sqrt{\frac{1}{5}}\!\,$

j₁=5/2, j₂=2

m=9/2

m₁, m₂=

	9/2
5/2, 2	$1\!\,$

m=7/2

m₁, m₂=

	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

m₁, m₂=

	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

m₁, m₂=

	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

m₁, m₂=

	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.^[5] 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. http://link.aip.org/link/?JMAPAQ/5/1723/1. Retrieved 2007-12-20.
^ 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. http://pdg.lbl.gov/2002/clebrpp.pdf. Retrieved 2007-12-20.
^ Mathar, Richard J. (2006-08-14). "SO(3) Clebsch Gordan coefficients" (text). http://www.strw.leidenuniv.nl/~mathar/progs/CGord. Retrieved 2007-12-20.
^ (2.41), p. 172, Quantum Mechanics: Foundations and Applications, Arno Bohm, M. Loewe, New York: Springer-Verlag, 3rd ed., 1993, ISBN 0387953302.
^ Alex, A.; M. Kalus, A. Huckleberry, and 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. doi:10.1063/1.3521562. http://link.aip.org/link/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-Gordon coefficients.
Web interface for tabulating SU(N) Clebsch-Gordan coefficients

Table of Clebsch–Gordan coefficients

Contents

Formulation

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

SU(N) Clebsch-Gordan coefficients

References

External links

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