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
,
,
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]
Contents
- 1 Formulation
- 2 A complete list [5]
- 2.1 j2=0
- 2.2 j1=<templatestyles src="Sfrac/styles.css" />1/2, j2=<templatestyles src="Sfrac/styles.css" />1/2
- 2.3 j1=1, j2=<templatestyles src="Sfrac/styles.css" />1/2
- 2.4 j1=1, j2=1
- 2.5 j1=<templatestyles src="Sfrac/styles.css" />3/2, j2=<templatestyles src="Sfrac/styles.css" />1/2
- 2.6 j1=<templatestyles src="Sfrac/styles.css" />3/2, j2=1
- 2.7 j1=<templatestyles src="Sfrac/styles.css" />3/2, j2=<templatestyles src="Sfrac/styles.css" />3/2
- 2.8 j1=2, j2=<templatestyles src="Sfrac/styles.css" />1/2
- 2.9 j1=2, j2=1
- 2.10 j1=2, j2=<templatestyles src="Sfrac/styles.css" />3/2
- 2.11 j1=2, j2=2
- 2.12 j1=<templatestyles src="Sfrac/styles.css" />5/2, j2=<templatestyles src="Sfrac/styles.css" />1/2
- 2.13 j1=<templatestyles src="Sfrac/styles.css" />5/2, j2=1
- 2.14 j1=<templatestyles src="Sfrac/styles.css" />5/2, j2=<templatestyles src="Sfrac/styles.css" />3/2
- 2.15 j1=<templatestyles src="Sfrac/styles.css" />5/2, j2=2
- 3 SU(N) Clebsch–Gordan coefficients
- 4 References
- 5 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](/w/images/math/c/1/e/c1e5925cf8d70b1c3af1acc0030291f6.png)
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}](/w/images/math/2/9/0/2900660bad91b0411f337df1d1bb6afb.png)
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 j1 < j2 are omitted. They may be calculated using the simple relations
.
and
.
A complete list [5]
j2=0
When j2 = 0, the Clebsch–Gordan coefficients are given by
.
j1=<templatestyles src="Sfrac/styles.css" />1/2, j2=<templatestyles src="Sfrac/styles.css" />1/2
m=1 |
j |
m1, m2 |
|
1 |
<templatestyles src="Sfrac/styles.css" />1/2, <templatestyles src="Sfrac/styles.css" />1/2 |
![1\!\,](/w/images/math/8/6/a/86a15e83dde1866a008672ce0596ff56.png) |
|
m=0 |
j |
m1, m2 |
|
1 |
0 |
<templatestyles src="Sfrac/styles.css" />1/2, -<templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{1}{2}}\!\,](/w/images/math/1/3/b/13bb77e63d2e64b4db48b884812dc993.png) |
![\sqrt{\frac{1}{2}}\!\,](/w/images/math/1/3/b/13bb77e63d2e64b4db48b884812dc993.png) |
-<templatestyles src="Sfrac/styles.css" />1/2, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{1}{2}}\!\,](/w/images/math/1/3/b/13bb77e63d2e64b4db48b884812dc993.png) |
![-\sqrt{\frac{1}{2}}\!\,](/w/images/math/f/8/2/f8251d2769bd457c5c22ac61b5c5256d.png) |
|
j1=1, j2=<templatestyles src="Sfrac/styles.css" />1/2
m=<templatestyles src="Sfrac/styles.css" />3/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />3/2 |
1, <templatestyles src="Sfrac/styles.css" />1/2 |
![1\!\,](/w/images/math/8/6/a/86a15e83dde1866a008672ce0596ff56.png) |
|
m=<templatestyles src="Sfrac/styles.css" />1/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />3/2 |
<templatestyles src="Sfrac/styles.css" />1/2 |
1, -<templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{1}{3}}\!\,](/w/images/math/6/9/d/69d8423b46466f17bf7d93715602d177.png) |
![\sqrt{\frac{2}{3}}\!\,](/w/images/math/9/e/b/9ebc75dd6a3d23b3c237f964fb5f2599.png) |
0, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{2}{3}}\!\,](/w/images/math/9/e/b/9ebc75dd6a3d23b3c237f964fb5f2599.png) |
![-\sqrt{\frac{1}{3}}\!\,](/w/images/math/6/a/9/6a93d3873ffc978fe679b2965bba5e28.png) |
|
j1=1, j2=1
m=2 |
j |
m1, m2 |
|
2 |
1, 1 |
![1\!\,](/w/images/math/8/6/a/86a15e83dde1866a008672ce0596ff56.png) |
|
j1=<templatestyles src="Sfrac/styles.css" />3/2, j2=<templatestyles src="Sfrac/styles.css" />1/2
m=2 |
j |
m1, m2 |
|
2 |
<templatestyles src="Sfrac/styles.css" />3/2, <templatestyles src="Sfrac/styles.css" />1/2 |
![1\!\,](/w/images/math/8/6/a/86a15e83dde1866a008672ce0596ff56.png) |
|
m=1 |
j |
m1, m2 |
|
2 |
1 |
<templatestyles src="Sfrac/styles.css" />3/2, -<templatestyles src="Sfrac/styles.css" />1/2 |
![\frac{1}{2}\!\,](/w/images/math/d/b/a/dba6a310ff4d31c9a80729fab3718b93.png) |
![\sqrt{\frac{3}{4}}\!\,](/w/images/math/7/5/4/754826b2da143ab20aa9046330cf8428.png) |
<templatestyles src="Sfrac/styles.css" />1/2, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{3}{4}}\!\,](/w/images/math/7/5/4/754826b2da143ab20aa9046330cf8428.png) |
![-\frac{1}{2}\!\,](/w/images/math/0/7/9/079b4f73717eba4cc09955245e304a89.png) |
|
m=0 |
j |
m1, m2 |
|
2 |
1 |
<templatestyles src="Sfrac/styles.css" />1/2, -<templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{1}{2}}\!\,](/w/images/math/1/3/b/13bb77e63d2e64b4db48b884812dc993.png) |
![\sqrt{\frac{1}{2}}\!\,](/w/images/math/1/3/b/13bb77e63d2e64b4db48b884812dc993.png) |
-<templatestyles src="Sfrac/styles.css" />1/2, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{1}{2}}\!\,](/w/images/math/1/3/b/13bb77e63d2e64b4db48b884812dc993.png) |
![-\sqrt{\frac{1}{2}}\!\,](/w/images/math/f/8/2/f8251d2769bd457c5c22ac61b5c5256d.png) |
|
j1=<templatestyles src="Sfrac/styles.css" />3/2, j2=1
m=<templatestyles src="Sfrac/styles.css" />5/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />5/2 |
<templatestyles src="Sfrac/styles.css" />3/2, 1 |
![1\!\,](/w/images/math/8/6/a/86a15e83dde1866a008672ce0596ff56.png) |
|
m=<templatestyles src="Sfrac/styles.css" />3/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />5/2 |
<templatestyles src="Sfrac/styles.css" />3/2 |
<templatestyles src="Sfrac/styles.css" />3/2, 0 |
![\sqrt{\frac{2}{5}}\!\,](/w/images/math/5/a/b/5abfb1d45958db4b8ac6459219b3b575.png) |
![\sqrt{\frac{3}{5}}\!\,](/w/images/math/8/c/f/8cf79fd9edd64913c14cc8b2732917a7.png) |
<templatestyles src="Sfrac/styles.css" />1/2, 1 |
![\sqrt{\frac{3}{5}}\!\,](/w/images/math/8/c/f/8cf79fd9edd64913c14cc8b2732917a7.png) |
![-\sqrt{\frac{2}{5}}\!\,](/w/images/math/9/4/b/94be4e0d7965fd9e1b8c96cb09632ed6.png) |
|
m=<templatestyles src="Sfrac/styles.css" />1/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />5/2 |
<templatestyles src="Sfrac/styles.css" />3/2 |
<templatestyles src="Sfrac/styles.css" />1/2 |
<templatestyles src="Sfrac/styles.css" />3/2, -1 |
![\sqrt{\frac{1}{10}}\!\,](/w/images/math/f/4/e/f4e28110bbca77a6d8cbbe314aa74059.png) |
![\sqrt{\frac{2}{5}}\!\,](/w/images/math/5/a/b/5abfb1d45958db4b8ac6459219b3b575.png) |
![\sqrt{\frac{1}{2}}\!\,](/w/images/math/1/3/b/13bb77e63d2e64b4db48b884812dc993.png) |
<templatestyles src="Sfrac/styles.css" />1/2, 0 |
![\sqrt{\frac{3}{5}}\!\,](/w/images/math/8/c/f/8cf79fd9edd64913c14cc8b2732917a7.png) |
![\sqrt{\frac{1}{15}}\!\,](/w/images/math/2/f/b/2fb67fa6d0d617d8c5a350c8329a5dbe.png) |
![-\sqrt{\frac{1}{3}}\!\,](/w/images/math/6/a/9/6a93d3873ffc978fe679b2965bba5e28.png) |
-<templatestyles src="Sfrac/styles.css" />1/2, 1 |
![\sqrt{\frac{3}{10}}\!\,](/w/images/math/b/1/a/b1a61fe830fff3195d1d9216610857bf.png) |
![-\sqrt{\frac{8}{15}}\!\,](/w/images/math/a/2/2/a22d64b54f8cbd9c0776745e861b536b.png) |
![\sqrt{\frac{1}{6}}\!\,](/w/images/math/0/e/f/0efc69df9d978b6fe3fd8c1a65244df8.png) |
|
j1=<templatestyles src="Sfrac/styles.css" />3/2, j2=<templatestyles src="Sfrac/styles.css" />3/2
m=3 |
j |
m1, m2 |
|
3 |
<templatestyles src="Sfrac/styles.css" />3/2, <templatestyles src="Sfrac/styles.css" />3/2 |
![1\!\,](/w/images/math/8/6/a/86a15e83dde1866a008672ce0596ff56.png) |
|
m=2 |
j |
m1, m2 |
|
3 |
2 |
<templatestyles src="Sfrac/styles.css" />3/2, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{1}{2}}\!\,](/w/images/math/1/3/b/13bb77e63d2e64b4db48b884812dc993.png) |
![\sqrt{\frac{1}{2}}\!\,](/w/images/math/1/3/b/13bb77e63d2e64b4db48b884812dc993.png) |
<templatestyles src="Sfrac/styles.css" />1/2, <templatestyles src="Sfrac/styles.css" />3/2 |
![\sqrt{\frac{1}{2}}\!\,](/w/images/math/1/3/b/13bb77e63d2e64b4db48b884812dc993.png) |
![-\sqrt{\frac{1}{2}}\!\,](/w/images/math/f/8/2/f8251d2769bd457c5c22ac61b5c5256d.png) |
|
m=1 |
j |
m1, m2 |
|
3 |
2 |
1 |
<templatestyles src="Sfrac/styles.css" />3/2, -<templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{1}{5}}\!\,](/w/images/math/7/e/d/7ed429b78e762155f263850df45e792e.png) |
![\sqrt{\frac{1}{2}}\!\,](/w/images/math/1/3/b/13bb77e63d2e64b4db48b884812dc993.png) |
![\sqrt{\frac{3}{10}}\!\,](/w/images/math/b/1/a/b1a61fe830fff3195d1d9216610857bf.png) |
<templatestyles src="Sfrac/styles.css" />1/2, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{3}{5}}\!\,](/w/images/math/8/c/f/8cf79fd9edd64913c14cc8b2732917a7.png) |
![0\!\,](/w/images/math/c/c/c/ccc912815b4a1b38fe8ece549c4f382c.png) |
![-\sqrt{\frac{2}{5}}\!\,](/w/images/math/9/4/b/94be4e0d7965fd9e1b8c96cb09632ed6.png) |
-<templatestyles src="Sfrac/styles.css" />1/2, <templatestyles src="Sfrac/styles.css" />3/2 |
![\sqrt{\frac{1}{5}}\!\,](/w/images/math/7/e/d/7ed429b78e762155f263850df45e792e.png) |
![-\sqrt{\frac{1}{2}}\!\,](/w/images/math/f/8/2/f8251d2769bd457c5c22ac61b5c5256d.png) |
![\sqrt{\frac{3}{10}}\!\,](/w/images/math/b/1/a/b1a61fe830fff3195d1d9216610857bf.png) |
|
m=0 |
j |
m1, m2 |
|
3 |
2 |
1 |
0 |
<templatestyles src="Sfrac/styles.css" />3/2, -<templatestyles src="Sfrac/styles.css" />3/2 |
![\sqrt{\frac{1}{20}}\!\,](/w/images/math/5/a/a/5aae440c005c629c55c4806cb48eb496.png) |
![\frac{1}{2}\!\,](/w/images/math/d/b/a/dba6a310ff4d31c9a80729fab3718b93.png) |
![\sqrt{\frac{9}{20}}\!\,](/w/images/math/4/c/8/4c81037c17c1886bdeb594a89063dd8d.png) |
![\frac{1}{2}\!\,](/w/images/math/d/b/a/dba6a310ff4d31c9a80729fab3718b93.png) |
<templatestyles src="Sfrac/styles.css" />1/2, -<templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{9}{20}}\!\,](/w/images/math/4/c/8/4c81037c17c1886bdeb594a89063dd8d.png) |
![\frac{1}{2}\!\,](/w/images/math/d/b/a/dba6a310ff4d31c9a80729fab3718b93.png) |
![-\sqrt{\frac{1}{20}}\!\,](/w/images/math/3/9/1/391c0a7abf6dbc74fec5f4d5eba100de.png) |
![-\frac{1}{2}\!\,](/w/images/math/0/7/9/079b4f73717eba4cc09955245e304a89.png) |
-<templatestyles src="Sfrac/styles.css" />1/2, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{9}{20}}\!\,](/w/images/math/4/c/8/4c81037c17c1886bdeb594a89063dd8d.png) |
![-\frac{1}{2}\!\,](/w/images/math/0/7/9/079b4f73717eba4cc09955245e304a89.png) |
![-\sqrt{\frac{1}{20}}\!\,](/w/images/math/3/9/1/391c0a7abf6dbc74fec5f4d5eba100de.png) |
![\frac{1}{2}\!\,](/w/images/math/d/b/a/dba6a310ff4d31c9a80729fab3718b93.png) |
-<templatestyles src="Sfrac/styles.css" />3/2, <templatestyles src="Sfrac/styles.css" />3/2 |
![\sqrt{\frac{1}{20}}\!\,](/w/images/math/5/a/a/5aae440c005c629c55c4806cb48eb496.png) |
![-\frac{1}{2}\!\,](/w/images/math/0/7/9/079b4f73717eba4cc09955245e304a89.png) |
![\sqrt{\frac{9}{20}}\!\,](/w/images/math/4/c/8/4c81037c17c1886bdeb594a89063dd8d.png) |
![-\frac{1}{2}\!\,](/w/images/math/0/7/9/079b4f73717eba4cc09955245e304a89.png) |
|
j1=2, j2=<templatestyles src="Sfrac/styles.css" />1/2
m=<templatestyles src="Sfrac/styles.css" />5/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />5/2 |
2, <templatestyles src="Sfrac/styles.css" />1/2 |
![1\!\,](/w/images/math/8/6/a/86a15e83dde1866a008672ce0596ff56.png) |
|
m=<templatestyles src="Sfrac/styles.css" />3/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />5/2 |
<templatestyles src="Sfrac/styles.css" />3/2 |
2, -<templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{1}{5}}\!\,](/w/images/math/7/e/d/7ed429b78e762155f263850df45e792e.png) |
![\sqrt{\frac{4}{5}}\!\,](/w/images/math/0/2/2/02258cd5f2e4c7761fc48e13f8a4b505.png) |
1, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{4}{5}}\!\,](/w/images/math/0/2/2/02258cd5f2e4c7761fc48e13f8a4b505.png) |
![-\sqrt{\frac{1}{5}}\!\,](/w/images/math/d/4/9/d49d3a14a0e499b25ffd53c2548dca5b.png) |
|
m=<templatestyles src="Sfrac/styles.css" />1/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />5/2 |
<templatestyles src="Sfrac/styles.css" />3/2 |
1, -<templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{2}{5}}\!\,](/w/images/math/5/a/b/5abfb1d45958db4b8ac6459219b3b575.png) |
![\sqrt{\frac{3}{5}}\!\,](/w/images/math/8/c/f/8cf79fd9edd64913c14cc8b2732917a7.png) |
0, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{3}{5}}\!\,](/w/images/math/8/c/f/8cf79fd9edd64913c14cc8b2732917a7.png) |
![-\sqrt{\frac{2}{5}}\!\,](/w/images/math/9/4/b/94be4e0d7965fd9e1b8c96cb09632ed6.png) |
|
j1=2, j2=1
m=3 |
j |
m1, m2 |
|
3 |
2, 1 |
![1\!\,](/w/images/math/8/6/a/86a15e83dde1866a008672ce0596ff56.png) |
|
j1=2, j2=<templatestyles src="Sfrac/styles.css" />3/2
m=<templatestyles src="Sfrac/styles.css" />7/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />7/2 |
2, <templatestyles src="Sfrac/styles.css" />3/2 |
![1\!\,](/w/images/math/8/6/a/86a15e83dde1866a008672ce0596ff56.png) |
|
m=<templatestyles src="Sfrac/styles.css" />5/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />7/2 |
<templatestyles src="Sfrac/styles.css" />5/2 |
2, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{3}{7}}\!\,](/w/images/math/6/8/4/6849635a9f6411a06768951e2b8e62ad.png) |
![\sqrt{\frac{4}{7}}\!\,](/w/images/math/5/3/9/5398363436eae509f10c01d657058165.png) |
1, <templatestyles src="Sfrac/styles.css" />3/2 |
![\sqrt{\frac{4}{7}}\!\,](/w/images/math/5/3/9/5398363436eae509f10c01d657058165.png) |
![-\sqrt{\frac{3}{7}}\!\,](/w/images/math/8/4/b/84be8baad01534d5f287b8713abb0b0c.png) |
|
m=<templatestyles src="Sfrac/styles.css" />3/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />7/2 |
<templatestyles src="Sfrac/styles.css" />5/2 |
<templatestyles src="Sfrac/styles.css" />3/2 |
2, -<templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{1}{7}}\!\,](/w/images/math/b/8/f/b8f7ce4251671a92cdd7745d04fdc8ad.png) |
![\sqrt{\frac{16}{35}}\!\,](/w/images/math/c/c/5/cc5f2e60402dec0d2abb4ef2bb56c120.png) |
![\sqrt{\frac{2}{5}}\!\,](/w/images/math/5/a/b/5abfb1d45958db4b8ac6459219b3b575.png) |
1, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{4}{7}}\!\,](/w/images/math/5/3/9/5398363436eae509f10c01d657058165.png) |
![\sqrt{\frac{1}{35}}\!\,](/w/images/math/c/7/9/c7943960d12bfc84bf84309ee29afcbf.png) |
![-\sqrt{\frac{2}{5}}\!\,](/w/images/math/9/4/b/94be4e0d7965fd9e1b8c96cb09632ed6.png) |
0, <templatestyles src="Sfrac/styles.css" />3/2 |
![\sqrt{\frac{2}{7}}\!\,](/w/images/math/4/5/7/457c0ce27b655eb427e7e06b8756abf6.png) |
![-\sqrt{\frac{18}{35}}\!\,](/w/images/math/b/9/9/b9949ddae86265b80d0235252076dee5.png) |
![\sqrt{\frac{1}{5}}\!\,](/w/images/math/7/e/d/7ed429b78e762155f263850df45e792e.png) |
|
m=<templatestyles src="Sfrac/styles.css" />1/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />7/2 |
<templatestyles src="Sfrac/styles.css" />5/2 |
<templatestyles src="Sfrac/styles.css" />3/2 |
<templatestyles src="Sfrac/styles.css" />1/2 |
2, -<templatestyles src="Sfrac/styles.css" />3/2 |
![\sqrt{\frac{1}{35}}\!\,](/w/images/math/c/7/9/c7943960d12bfc84bf84309ee29afcbf.png) |
![\sqrt{\frac{6}{35}}\!\,](/w/images/math/0/8/a/08a6d40089df5eb0121d160d89ea7fc2.png) |
![\sqrt{\frac{2}{5}}\!\,](/w/images/math/5/a/b/5abfb1d45958db4b8ac6459219b3b575.png) |
![\sqrt{\frac{2}{5}}\!\,](/w/images/math/5/a/b/5abfb1d45958db4b8ac6459219b3b575.png) |
1, -<templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{12}{35}}\!\,](/w/images/math/d/e/5/de541051faff4df2871ed42016aa3cec.png) |
![\sqrt{\frac{5}{14}}\!\,](/w/images/math/a/7/7/a77011ccde4c51c7e1d382084de86965.png) |
![0\!\,](/w/images/math/c/c/c/ccc912815b4a1b38fe8ece549c4f382c.png) |
![-\sqrt{\frac{3}{10}}\!\,](/w/images/math/e/9/6/e961d2795f7eae595d542288fb11195c.png) |
0, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{18}{35}}\!\,](/w/images/math/c/6/1/c61e9606a7cc621d8376144346caaf1c.png) |
![-\sqrt{\frac{3}{35}}\!\,](/w/images/math/e/1/b/e1b259522f9d036b4051c4909ddc6a21.png) |
![-\sqrt{\frac{1}{5}}\!\,](/w/images/math/d/4/9/d49d3a14a0e499b25ffd53c2548dca5b.png) |
![\sqrt{\frac{1}{5}}\!\,](/w/images/math/7/e/d/7ed429b78e762155f263850df45e792e.png) |
-1, <templatestyles src="Sfrac/styles.css" />3/2 |
![\sqrt{\frac{4}{35}}\!\,](/w/images/math/1/8/4/184b1687127acec44fb86457c6a2f914.png) |
![-\sqrt{\frac{27}{70}}\!\,](/w/images/math/5/2/8/528f83c4e9f53e83e19d1cd4b0ed3a92.png) |
![\sqrt{\frac{2}{5}}\!\,](/w/images/math/5/a/b/5abfb1d45958db4b8ac6459219b3b575.png) |
![-\sqrt{\frac{1}{10}}\!\,](/w/images/math/b/b/8/bb83985be8df8c1c7b1a27b47a0828b0.png) |
|
j1=2, j2=2
m=4 |
j |
m1, m2 |
|
4 |
2, 2 |
![1\!\,](/w/images/math/8/6/a/86a15e83dde1866a008672ce0596ff56.png) |
|
m=1 |
j |
m1, m2 |
|
4 |
3 |
2 |
1 |
2, -1 |
![\sqrt{\frac{1}{14}}\!\,](/w/images/math/a/e/5/ae52f99fcd4280c1739470e0003abf54.png) |
![\sqrt{\frac{3}{10}}\!\,](/w/images/math/b/1/a/b1a61fe830fff3195d1d9216610857bf.png) |
![\sqrt{\frac{3}{7}}\!\,](/w/images/math/6/8/4/6849635a9f6411a06768951e2b8e62ad.png) |
![\sqrt{\frac{1}{5}}\!\,](/w/images/math/7/e/d/7ed429b78e762155f263850df45e792e.png) |
1, 0 |
![\sqrt{\frac{3}{7}}\!\,](/w/images/math/6/8/4/6849635a9f6411a06768951e2b8e62ad.png) |
![\sqrt{\frac{1}{5}}\!\,](/w/images/math/7/e/d/7ed429b78e762155f263850df45e792e.png) |
![-\sqrt{\frac{1}{14}}\!\,](/w/images/math/9/f/0/9f0927591796a57f074c6d0b1d5077fc.png) |
![-\sqrt{\frac{3}{10}}\!\,](/w/images/math/e/9/6/e961d2795f7eae595d542288fb11195c.png) |
0, 1 |
![\sqrt{\frac{3}{7}}\!\,](/w/images/math/6/8/4/6849635a9f6411a06768951e2b8e62ad.png) |
![-\sqrt{\frac{1}{5}}\!\,](/w/images/math/d/4/9/d49d3a14a0e499b25ffd53c2548dca5b.png) |
![-\sqrt{\frac{1}{14}}\!\,](/w/images/math/9/f/0/9f0927591796a57f074c6d0b1d5077fc.png) |
![\sqrt{\frac{3}{10}}\!\,](/w/images/math/b/1/a/b1a61fe830fff3195d1d9216610857bf.png) |
-1, 2 |
![\sqrt{\frac{1}{14}}\!\,](/w/images/math/a/e/5/ae52f99fcd4280c1739470e0003abf54.png) |
![-\sqrt{\frac{3}{10}}\!\,](/w/images/math/e/9/6/e961d2795f7eae595d542288fb11195c.png) |
![\sqrt{\frac{3}{7}}\!\,](/w/images/math/6/8/4/6849635a9f6411a06768951e2b8e62ad.png) |
![-\sqrt{\frac{1}{5}}\!\,](/w/images/math/d/4/9/d49d3a14a0e499b25ffd53c2548dca5b.png) |
|
m=0 |
j |
m1, m2 |
|
4 |
3 |
2 |
1 |
0 |
2, -2 |
![\sqrt{\frac{1}{70}}\!\,](/w/images/math/7/8/0/78001e490fbf43e597ec8dc0936c6232.png) |
![\sqrt{\frac{1}{10}}\!\,](/w/images/math/f/4/e/f4e28110bbca77a6d8cbbe314aa74059.png) |
![\sqrt{\frac{2}{7}}\!\,](/w/images/math/4/5/7/457c0ce27b655eb427e7e06b8756abf6.png) |
![\sqrt{\frac{2}{5}}\!\,](/w/images/math/5/a/b/5abfb1d45958db4b8ac6459219b3b575.png) |
![\sqrt{\frac{1}{5}}\!\,](/w/images/math/7/e/d/7ed429b78e762155f263850df45e792e.png) |
1, -1 |
![\sqrt{\frac{8}{35}}\!\,](/w/images/math/5/5/7/5571ec984ea1cbaef008900bbf1f8ba7.png) |
![\sqrt{\frac{2}{5}}\!\,](/w/images/math/5/a/b/5abfb1d45958db4b8ac6459219b3b575.png) |
![\sqrt{\frac{1}{14}}\!\,](/w/images/math/a/e/5/ae52f99fcd4280c1739470e0003abf54.png) |
![-\sqrt{\frac{1}{10}}\!\,](/w/images/math/b/b/8/bb83985be8df8c1c7b1a27b47a0828b0.png) |
![-\sqrt{\frac{1}{5}}\!\,](/w/images/math/d/4/9/d49d3a14a0e499b25ffd53c2548dca5b.png) |
0, 0 |
![\sqrt{\frac{18}{35}}\!\,](/w/images/math/c/6/1/c61e9606a7cc621d8376144346caaf1c.png) |
![0\!\,](/w/images/math/c/c/c/ccc912815b4a1b38fe8ece549c4f382c.png) |
![-\sqrt{\frac{2}{7}}\!\,](/w/images/math/0/6/9/0699afee2b348904d4a5b1ac1099d3e9.png) |
![0\!\,](/w/images/math/c/c/c/ccc912815b4a1b38fe8ece549c4f382c.png) |
![\sqrt{\frac{1}{5}}\!\,](/w/images/math/7/e/d/7ed429b78e762155f263850df45e792e.png) |
-1, 1 |
![\sqrt{\frac{8}{35}}\!\,](/w/images/math/5/5/7/5571ec984ea1cbaef008900bbf1f8ba7.png) |
![-\sqrt{\frac{2}{5}}\!\,](/w/images/math/9/4/b/94be4e0d7965fd9e1b8c96cb09632ed6.png) |
![\sqrt{\frac{1}{14}}\!\,](/w/images/math/a/e/5/ae52f99fcd4280c1739470e0003abf54.png) |
![\sqrt{\frac{1}{10}}\!\,](/w/images/math/f/4/e/f4e28110bbca77a6d8cbbe314aa74059.png) |
![-\sqrt{\frac{1}{5}}\!\,](/w/images/math/d/4/9/d49d3a14a0e499b25ffd53c2548dca5b.png) |
-2, 2 |
![\sqrt{\frac{1}{70}}\!\,](/w/images/math/7/8/0/78001e490fbf43e597ec8dc0936c6232.png) |
![-\sqrt{\frac{1}{10}}\!\,](/w/images/math/b/b/8/bb83985be8df8c1c7b1a27b47a0828b0.png) |
![\sqrt{\frac{2}{7}}\!\,](/w/images/math/4/5/7/457c0ce27b655eb427e7e06b8756abf6.png) |
![-\sqrt{\frac{2}{5}}\!\,](/w/images/math/9/4/b/94be4e0d7965fd9e1b8c96cb09632ed6.png) |
![\sqrt{\frac{1}{5}}\!\,](/w/images/math/7/e/d/7ed429b78e762155f263850df45e792e.png) |
|
j1=<templatestyles src="Sfrac/styles.css" />5/2, j2=<templatestyles src="Sfrac/styles.css" />1/2
m=3 |
j |
m1, m2 |
|
3 |
<templatestyles src="Sfrac/styles.css" />5/2, <templatestyles src="Sfrac/styles.css" />1/2 |
![1\!\,](/w/images/math/8/6/a/86a15e83dde1866a008672ce0596ff56.png) |
|
m=2 |
j |
m1, m2 |
|
3 |
2 |
<templatestyles src="Sfrac/styles.css" />5/2, -<templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{1}{6}}\!\,](/w/images/math/0/e/f/0efc69df9d978b6fe3fd8c1a65244df8.png) |
![\sqrt{\frac{5}{6}}\!\,](/w/images/math/1/a/8/1a83c0371112629050a7f586f856addb.png) |
<templatestyles src="Sfrac/styles.css" />3/2, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{5}{6}}\!\,](/w/images/math/1/a/8/1a83c0371112629050a7f586f856addb.png) |
![-\sqrt{\frac{1}{6}}\!\,](/w/images/math/f/8/3/f831bf6e7ae6a136fdeb4863ea2db74b.png) |
|
m=1 |
j |
m1, m2 |
|
3 |
2 |
<templatestyles src="Sfrac/styles.css" />3/2, -<templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{1}{3}}\!\,](/w/images/math/6/9/d/69d8423b46466f17bf7d93715602d177.png) |
![\sqrt{\frac{2}{3}}\!\,](/w/images/math/9/e/b/9ebc75dd6a3d23b3c237f964fb5f2599.png) |
<templatestyles src="Sfrac/styles.css" />1/2, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{2}{3}}\!\,](/w/images/math/9/e/b/9ebc75dd6a3d23b3c237f964fb5f2599.png) |
![-\sqrt{\frac{1}{3}}\!\,](/w/images/math/6/a/9/6a93d3873ffc978fe679b2965bba5e28.png) |
|
m=0 |
j |
m1, m2 |
|
3 |
2 |
<templatestyles src="Sfrac/styles.css" />1/2, -<templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{1}{2}}\!\,](/w/images/math/1/3/b/13bb77e63d2e64b4db48b884812dc993.png) |
![\sqrt{\frac{1}{2}}\!\,](/w/images/math/1/3/b/13bb77e63d2e64b4db48b884812dc993.png) |
-<templatestyles src="Sfrac/styles.css" />1/2, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{1}{2}}\!\,](/w/images/math/1/3/b/13bb77e63d2e64b4db48b884812dc993.png) |
![-\sqrt{\frac{1}{2}}\!\,](/w/images/math/f/8/2/f8251d2769bd457c5c22ac61b5c5256d.png) |
|
j1=<templatestyles src="Sfrac/styles.css" />5/2, j2=1
m=<templatestyles src="Sfrac/styles.css" />7/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />7/2 |
<templatestyles src="Sfrac/styles.css" />5/2, 1 |
![1\!\,](/w/images/math/8/6/a/86a15e83dde1866a008672ce0596ff56.png) |
|
m=<templatestyles src="Sfrac/styles.css" />5/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />7/2 |
<templatestyles src="Sfrac/styles.css" />5/2 |
<templatestyles src="Sfrac/styles.css" />5/2, 0 |
![\sqrt{\frac{2}{7}}\!\,](/w/images/math/4/5/7/457c0ce27b655eb427e7e06b8756abf6.png) |
![\sqrt{\frac{5}{7}}\!\,](/w/images/math/f/a/d/fadd8da6d65efcb6eddb9b77d1a82dc3.png) |
<templatestyles src="Sfrac/styles.css" />3/2, 1 |
![\sqrt{\frac{5}{7}}\!\,](/w/images/math/f/a/d/fadd8da6d65efcb6eddb9b77d1a82dc3.png) |
![-\sqrt{\frac{2}{7}}\!\,](/w/images/math/0/6/9/0699afee2b348904d4a5b1ac1099d3e9.png) |
|
m=<templatestyles src="Sfrac/styles.css" />3/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />7/2 |
<templatestyles src="Sfrac/styles.css" />5/2 |
<templatestyles src="Sfrac/styles.css" />3/2 |
<templatestyles src="Sfrac/styles.css" />5/2, -1 |
![\sqrt{\frac{1}{21}}\!\,](/w/images/math/8/5/f/85fb2022650ca81bb9dea38de99a86b1.png) |
![\sqrt{\frac{2}{7}}\!\,](/w/images/math/4/5/7/457c0ce27b655eb427e7e06b8756abf6.png) |
![\sqrt{\frac{2}{3}}\!\,](/w/images/math/9/e/b/9ebc75dd6a3d23b3c237f964fb5f2599.png) |
<templatestyles src="Sfrac/styles.css" />3/2, 0 |
![\sqrt{\frac{10}{21}}\!\,](/w/images/math/8/d/4/8d4b160168745675ad32c6b5ebcccc36.png) |
![\sqrt{\frac{9}{35}}\!\,](/w/images/math/8/a/5/8a5cff4a101b8a4c40970356dde2f7d7.png) |
![-\sqrt{\frac{4}{15}}\!\,](/w/images/math/9/2/5/925541aab8866c34ce8121d61581f82b.png) |
<templatestyles src="Sfrac/styles.css" />1/2, 1 |
![\sqrt{\frac{10}{21}}\!\,](/w/images/math/8/d/4/8d4b160168745675ad32c6b5ebcccc36.png) |
![-\sqrt{\frac{16}{35}}\!\,](/w/images/math/e/a/b/eab19d99d81824e76f6a11a1fb86aefb.png) |
![\sqrt{\frac{1}{15}}\!\,](/w/images/math/2/f/b/2fb67fa6d0d617d8c5a350c8329a5dbe.png) |
|
m=<templatestyles src="Sfrac/styles.css" />1/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />7/2 |
<templatestyles src="Sfrac/styles.css" />5/2 |
<templatestyles src="Sfrac/styles.css" />3/2 |
<templatestyles src="Sfrac/styles.css" />3/2, -1 |
![\sqrt{\frac{1}{7}}\!\,](/w/images/math/b/8/f/b8f7ce4251671a92cdd7745d04fdc8ad.png) |
![\sqrt{\frac{16}{35}}\!\,](/w/images/math/c/c/5/cc5f2e60402dec0d2abb4ef2bb56c120.png) |
![\sqrt{\frac{2}{5}}\!\,](/w/images/math/5/a/b/5abfb1d45958db4b8ac6459219b3b575.png) |
<templatestyles src="Sfrac/styles.css" />1/2, 0 |
![\sqrt{\frac{4}{7}}\!\,](/w/images/math/5/3/9/5398363436eae509f10c01d657058165.png) |
![\sqrt{\frac{1}{35}}\!\,](/w/images/math/c/7/9/c7943960d12bfc84bf84309ee29afcbf.png) |
![-\sqrt{\frac{2}{5}}\!\,](/w/images/math/9/4/b/94be4e0d7965fd9e1b8c96cb09632ed6.png) |
-<templatestyles src="Sfrac/styles.css" />1/2, 1 |
![\sqrt{\frac{2}{7}}\!\,](/w/images/math/4/5/7/457c0ce27b655eb427e7e06b8756abf6.png) |
![-\sqrt{\frac{18}{35}}\!\,](/w/images/math/b/9/9/b9949ddae86265b80d0235252076dee5.png) |
![\sqrt{\frac{1}{5}}\!\,](/w/images/math/7/e/d/7ed429b78e762155f263850df45e792e.png) |
|
j1=<templatestyles src="Sfrac/styles.css" />5/2, j2=<templatestyles src="Sfrac/styles.css" />3/2
m=4 |
j |
m1, m2 |
|
4 |
<templatestyles src="Sfrac/styles.css" />5/2, <templatestyles src="Sfrac/styles.css" />3/2 |
![1\!\,](/w/images/math/8/6/a/86a15e83dde1866a008672ce0596ff56.png) |
|
m=3 |
j |
m1, m2 |
|
4 |
3 |
<templatestyles src="Sfrac/styles.css" />5/2, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{3}{8}}\!\,](/w/images/math/d/d/d/ddd99840822ce59b4bb50c5e1ce380df.png) |
![\sqrt{\frac{5}{8}}\!\,](/w/images/math/7/a/1/7a1923a8647290ff1e06192f78dea0b9.png) |
<templatestyles src="Sfrac/styles.css" />3/2, <templatestyles src="Sfrac/styles.css" />3/2 |
![\sqrt{\frac{5}{8}}\!\,](/w/images/math/7/a/1/7a1923a8647290ff1e06192f78dea0b9.png) |
![-\sqrt{\frac{3}{8}}\!\,](/w/images/math/a/2/7/a278c5b2e95651c3aa2117c5c0e6862c.png) |
|
m=2 |
j |
m1, m2 |
|
4 |
3 |
2 |
<templatestyles src="Sfrac/styles.css" />5/2, -<templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{3}{28}}\!\,](/w/images/math/2/d/2/2d22a61f81e99f93b5b6c53cf1e17805.png) |
![\sqrt{\frac{5}{12}}\!\,](/w/images/math/3/4/7/3477c98518ca23b833a7d736c99e8205.png) |
![\sqrt{\frac{10}{21}}\!\,](/w/images/math/8/d/4/8d4b160168745675ad32c6b5ebcccc36.png) |
<templatestyles src="Sfrac/styles.css" />3/2, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{15}{28}}\!\,](/w/images/math/0/8/d/08d96efd648255750a68848de938fc18.png) |
![\sqrt{\frac{1}{12}}\!\,](/w/images/math/2/d/3/2d30ab1bb1399639ee7856802c6c23fe.png) |
![-\sqrt{\frac{8}{21}}\!\,](/w/images/math/f/6/a/f6af7102528d34f3330ddb2730bb9981.png) |
<templatestyles src="Sfrac/styles.css" />1/2, <templatestyles src="Sfrac/styles.css" />3/2 |
![\sqrt{\frac{5}{14}}\!\,](/w/images/math/a/7/7/a77011ccde4c51c7e1d382084de86965.png) |
![-\sqrt{\frac{1}{2}}\!\,](/w/images/math/f/8/2/f8251d2769bd457c5c22ac61b5c5256d.png) |
![\sqrt{\frac{1}{7}}\!\,](/w/images/math/b/8/f/b8f7ce4251671a92cdd7745d04fdc8ad.png) |
|
m=1 |
j |
m1, m2 |
|
4 |
3 |
2 |
1 |
<templatestyles src="Sfrac/styles.css" />5/2, -<templatestyles src="Sfrac/styles.css" />3/2 |
![\sqrt{\frac{1}{56}}\!\,](/w/images/math/3/e/b/3ebe4817b6b7343805f690b33b1395e6.png) |
![\sqrt{\frac{1}{8}}\!\,](/w/images/math/4/8/b/48b145392693e53097c503113a027d61.png) |
![\sqrt{\frac{5}{14}}\!\,](/w/images/math/a/7/7/a77011ccde4c51c7e1d382084de86965.png) |
![\sqrt{\frac{1}{2}}\!\,](/w/images/math/1/3/b/13bb77e63d2e64b4db48b884812dc993.png) |
<templatestyles src="Sfrac/styles.css" />3/2, -<templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{15}{56}}\!\,](/w/images/math/9/6/b/96bbd71d1ea69c466924f2e1d95fb942.png) |
![\sqrt{\frac{49}{120}}\!\,](/w/images/math/0/f/c/0fcee4ad6f44999fe5b160b5a7e285d4.png) |
![\sqrt{\frac{1}{42}}\!\,](/w/images/math/f/a/2/fa2b59cd185248d0c871ed09f6290dfb.png) |
![-\sqrt{\frac{3}{10}}\!\,](/w/images/math/e/9/6/e961d2795f7eae595d542288fb11195c.png) |
<templatestyles src="Sfrac/styles.css" />1/2, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{15}{28}}\!\,](/w/images/math/0/8/d/08d96efd648255750a68848de938fc18.png) |
![-\sqrt{\frac{1}{60}}\!\,](/w/images/math/b/d/c/bdc06f80d6e937f2ce5520bdcb90658e.png) |
![-\sqrt{\frac{25}{84}}\!\,](/w/images/math/7/2/2/7227bdd332cfb094534f6f8c8b5c2b38.png) |
![\sqrt{\frac{3}{20}}\!\,](/w/images/math/9/7/9/979d287d2e6988640758f1ae4afa6bff.png) |
-<templatestyles src="Sfrac/styles.css" />1/2, <templatestyles src="Sfrac/styles.css" />3/2 |
![\sqrt{\frac{5}{28}}\!\,](/w/images/math/7/2/c/72cf558539b684325288d17082588ac7.png) |
![-\sqrt{\frac{9}{20}}\!\,](/w/images/math/8/1/0/810566799c0d33857414c3a7b252dead.png) |
![\sqrt{\frac{9}{28}}\!\,](/w/images/math/1/b/0/1b0430d99f69a409bc095978719a667e.png) |
![-\sqrt{\frac{1}{20}}\!\,](/w/images/math/3/9/1/391c0a7abf6dbc74fec5f4d5eba100de.png) |
|
m=0 |
j |
m1, m2 |
|
4 |
3 |
2 |
1 |
<templatestyles src="Sfrac/styles.css" />3/2, -<templatestyles src="Sfrac/styles.css" />3/2 |
![\sqrt{\frac{1}{14}}\!\,](/w/images/math/a/e/5/ae52f99fcd4280c1739470e0003abf54.png) |
![\sqrt{\frac{3}{10}}\!\,](/w/images/math/b/1/a/b1a61fe830fff3195d1d9216610857bf.png) |
![\sqrt{\frac{3}{7}}\!\,](/w/images/math/6/8/4/6849635a9f6411a06768951e2b8e62ad.png) |
![\sqrt{\frac{1}{5}}\!\,](/w/images/math/7/e/d/7ed429b78e762155f263850df45e792e.png) |
<templatestyles src="Sfrac/styles.css" />1/2, -<templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{3}{7}}\!\,](/w/images/math/6/8/4/6849635a9f6411a06768951e2b8e62ad.png) |
![\sqrt{\frac{1}{5}}\!\,](/w/images/math/7/e/d/7ed429b78e762155f263850df45e792e.png) |
![-\sqrt{\frac{1}{14}}\!\,](/w/images/math/9/f/0/9f0927591796a57f074c6d0b1d5077fc.png) |
![-\sqrt{\frac{3}{10}}\!\,](/w/images/math/e/9/6/e961d2795f7eae595d542288fb11195c.png) |
-<templatestyles src="Sfrac/styles.css" />1/2, <templatestyles src="Sfrac/styles.css" />1/2 |
![\sqrt{\frac{3}{7}}\!\,](/w/images/math/6/8/4/6849635a9f6411a06768951e2b8e62ad.png) |
![-\sqrt{\frac{1}{5}}\!\,](/w/images/math/d/4/9/d49d3a14a0e499b25ffd53c2548dca5b.png) |
![-\sqrt{\frac{1}{14}}\!\,](/w/images/math/9/f/0/9f0927591796a57f074c6d0b1d5077fc.png) |
![\sqrt{\frac{3}{10}}\!\,](/w/images/math/b/1/a/b1a61fe830fff3195d1d9216610857bf.png) |
-<templatestyles src="Sfrac/styles.css" />3/2, <templatestyles src="Sfrac/styles.css" />3/2 |
![\sqrt{\frac{1}{14}}\!\,](/w/images/math/a/e/5/ae52f99fcd4280c1739470e0003abf54.png) |
![-\sqrt{\frac{3}{10}}\!\,](/w/images/math/e/9/6/e961d2795f7eae595d542288fb11195c.png) |
![\sqrt{\frac{3}{7}}\!\,](/w/images/math/6/8/4/6849635a9f6411a06768951e2b8e62ad.png) |
![-\sqrt{\frac{1}{5}}\!\,](/w/images/math/d/4/9/d49d3a14a0e499b25ffd53c2548dca5b.png) |
|
j1=<templatestyles src="Sfrac/styles.css" />5/2, j2=2
m=<templatestyles src="Sfrac/styles.css" />9/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />9/2 |
<templatestyles src="Sfrac/styles.css" />5/2, 2 |
![1\!\,](/w/images/math/8/6/a/86a15e83dde1866a008672ce0596ff56.png) |
|
m=<templatestyles src="Sfrac/styles.css" />7/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />9/2 |
<templatestyles src="Sfrac/styles.css" />7/2 |
<templatestyles src="Sfrac/styles.css" />5/2, 1 |
![\frac{2}{3}\!\,](/w/images/math/2/3/5/235d723e66bfd1eed7d1ac9a5d58c2f3.png) |
![\sqrt{\frac{5}{9}}\!\,](/w/images/math/e/3/4/e34748d3a49611a9aca5f597e45cbf4d.png) |
<templatestyles src="Sfrac/styles.css" />3/2, 2 |
![\sqrt{\frac{5}{9}}\!\,](/w/images/math/e/3/4/e34748d3a49611a9aca5f597e45cbf4d.png) |
![-\frac{2}{3}\!\,](/w/images/math/5/4/1/5416a7af2997aa250328a77bb5435409.png) |
|
m=<templatestyles src="Sfrac/styles.css" />5/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />9/2 |
<templatestyles src="Sfrac/styles.css" />7/2 |
<templatestyles src="Sfrac/styles.css" />5/2 |
<templatestyles src="Sfrac/styles.css" />5/2, 0 |
![\sqrt{\frac{1}{6}}\!\,](/w/images/math/0/e/f/0efc69df9d978b6fe3fd8c1a65244df8.png) |
![\sqrt{\frac{10}{21}}\!\,](/w/images/math/8/d/4/8d4b160168745675ad32c6b5ebcccc36.png) |
![\sqrt{\frac{5}{14}}\!\,](/w/images/math/a/7/7/a77011ccde4c51c7e1d382084de86965.png) |
<templatestyles src="Sfrac/styles.css" />3/2, 1 |
![\sqrt{\frac{5}{9}}\!\,](/w/images/math/e/3/4/e34748d3a49611a9aca5f597e45cbf4d.png) |
![\sqrt{\frac{1}{63}}\!\,](/w/images/math/3/f/d/3fd2ec6ddc76e6af2b42897e94050319.png) |
![-\sqrt{\frac{3}{7}}\!\,](/w/images/math/8/4/b/84be8baad01534d5f287b8713abb0b0c.png) |
<templatestyles src="Sfrac/styles.css" />1/2, 2 |
![\sqrt{\frac{5}{18}}\!\,](/w/images/math/6/e/b/6eb4ba699b4d8caf9b5e0003842b565b.png) |
![-\sqrt{\frac{32}{63}}\!\,](/w/images/math/6/d/2/6d24d75229d7fc8888a007968c3dc5e4.png) |
![\sqrt{\frac{3}{14}}\!\,](/w/images/math/6/0/3/60322287a304d0ce8090bb1a13b49930.png) |
|
m=<templatestyles src="Sfrac/styles.css" />3/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />9/2 |
<templatestyles src="Sfrac/styles.css" />7/2 |
<templatestyles src="Sfrac/styles.css" />5/2 |
<templatestyles src="Sfrac/styles.css" />3/2 |
<templatestyles src="Sfrac/styles.css" />5/2, -1 |
![\sqrt{\frac{1}{21}}\!\,](/w/images/math/8/5/f/85fb2022650ca81bb9dea38de99a86b1.png) |
![\sqrt{\frac{5}{21}}\!\,](/w/images/math/7/9/1/791daff90d81d20b5d204fa8cd423e8b.png) |
![\sqrt{\frac{3}{7}}\!\,](/w/images/math/6/8/4/6849635a9f6411a06768951e2b8e62ad.png) |
![\sqrt{\frac{2}{7}}\!\,](/w/images/math/4/5/7/457c0ce27b655eb427e7e06b8756abf6.png) |
<templatestyles src="Sfrac/styles.css" />3/2, 0 |
![\sqrt{\frac{5}{14}}\!\,](/w/images/math/a/7/7/a77011ccde4c51c7e1d382084de86965.png) |
![\sqrt{\frac{2}{7}}\!\,](/w/images/math/4/5/7/457c0ce27b655eb427e7e06b8756abf6.png) |
![-\sqrt{\frac{1}{70}}\!\,](/w/images/math/a/0/5/a05062d28a4977de745ec89e7ebef1d8.png) |
![-\sqrt{\frac{12}{35}}\!\,](/w/images/math/c/c/9/cc9236bdaa17126b41810134d9ebf128.png) |
<templatestyles src="Sfrac/styles.css" />1/2, 1 |
![\sqrt{\frac{10}{21}}\!\,](/w/images/math/8/d/4/8d4b160168745675ad32c6b5ebcccc36.png) |
![-\sqrt{\frac{2}{21}}\!\,](/w/images/math/7/f/e/7fe4df7bfd2054aabc6772c48d74ed33.png) |
![-\sqrt{\frac{6}{35}}\!\,](/w/images/math/5/d/b/5db0fe60d32d97490664767d625ac8b6.png) |
![\sqrt{\frac{9}{35}}\!\,](/w/images/math/8/a/5/8a5cff4a101b8a4c40970356dde2f7d7.png) |
-<templatestyles src="Sfrac/styles.css" />1/2, 2 |
![\sqrt{\frac{5}{42}}\!\,](/w/images/math/3/2/8/328ec15af46d9b4a77dc6a2898ac0a10.png) |
![-\sqrt{\frac{8}{21}}\!\,](/w/images/math/f/6/a/f6af7102528d34f3330ddb2730bb9981.png) |
![\sqrt{\frac{27}{70}}\!\,](/w/images/math/8/a/e/8ae6fd11dfe864b8cb7218eef01f63d9.png) |
![-\sqrt{\frac{4}{35}}\!\,](/w/images/math/c/0/5/c05c9d147796d74cbe6cbb359b91d171.png) |
|
m=<templatestyles src="Sfrac/styles.css" />1/2 |
j |
m1, m2 |
|
<templatestyles src="Sfrac/styles.css" />9/2 |
<templatestyles src="Sfrac/styles.css" />7/2 |
<templatestyles src="Sfrac/styles.css" />5/2 |
<templatestyles src="Sfrac/styles.css" />3/2 |
<templatestyles src="Sfrac/styles.css" />1/2 |
<templatestyles src="Sfrac/styles.css" />5/2, -2 |
![\sqrt{\frac{1}{126}}\!\,](/w/images/math/5/5/a/55a8cd88cd323c6228f9fa7059d8f6d7.png) |
![\sqrt{\frac{4}{63}}\!\,](/w/images/math/0/6/f/06fabef124bf8704fe249b87a48ebc33.png) |
![\sqrt{\frac{3}{14}}\!\,](/w/images/math/6/0/3/60322287a304d0ce8090bb1a13b49930.png) |
![\sqrt{\frac{8}{21}}\!\,](/w/images/math/2/a/5/2a5f22787b099a69d2084b57c98a1e4a.png) |
![\sqrt{\frac{1}{3}}\!\,](/w/images/math/6/9/d/69d8423b46466f17bf7d93715602d177.png) |
<templatestyles src="Sfrac/styles.css" />3/2, -1 |
![\sqrt{\frac{10}{63}}\!\,](/w/images/math/8/c/b/8cbb8049d19461866d522c2e70810ac8.png) |
![\sqrt{\frac{121}{315}}\!\,](/w/images/math/d/b/e/dbe2e0c192d728165a151fb1c9f3cd7f.png) |
![\sqrt{\frac{6}{35}}\!\,](/w/images/math/0/8/a/08a6d40089df5eb0121d160d89ea7fc2.png) |
![-\sqrt{\frac{2}{105}}\!\,](/w/images/math/1/2/b/12b2663c05bf761547a130fb6bee959a.png) |
![-\sqrt{\frac{4}{15}}\!\,](/w/images/math/9/2/5/925541aab8866c34ce8121d61581f82b.png) |
<templatestyles src="Sfrac/styles.css" />1/2, 0 |
![\sqrt{\frac{10}{21}}\!\,](/w/images/math/8/d/4/8d4b160168745675ad32c6b5ebcccc36.png) |
![\sqrt{\frac{4}{105}}\!\,](/w/images/math/8/9/1/891db4164a75490757f55f71146163cd.png) |
![-\sqrt{\frac{8}{35}}\!\,](/w/images/math/c/d/5/cd5044cedf60f9c12100c6bfa78cdc22.png) |
![-\sqrt{\frac{2}{35}}\!\,](/w/images/math/f/1/7/f173c642f7587e3e322c9bc90a441660.png) |
![\sqrt{\frac{1}{5}}\!\,](/w/images/math/7/e/d/7ed429b78e762155f263850df45e792e.png) |
-<templatestyles src="Sfrac/styles.css" />1/2, 1 |
![\sqrt{\frac{20}{63}}\!\,](/w/images/math/9/c/7/9c7387da98e2bb8d6387e7056acdba22.png) |
![-\sqrt{\frac{14}{45}}\!\,](/w/images/math/c/d/e/cded20961deeb53a248592a4b9b6bc03.png) |
![0\!\,](/w/images/math/c/c/c/ccc912815b4a1b38fe8ece549c4f382c.png) |
![\sqrt{\frac{5}{21}}\!\,](/w/images/math/7/9/1/791daff90d81d20b5d204fa8cd423e8b.png) |
![-\sqrt{\frac{2}{15}}\!\,](/w/images/math/a/1/c/a1cb685ef4459e03d9faeb7b3ceb06d0.png) |
-<templatestyles src="Sfrac/styles.css" />3/2, 2 |
![\sqrt{\frac{5}{126}}\!\,](/w/images/math/d/8/b/d8bc74e25b1cbc4ddf333d823c12f2ea.png) |
![-\sqrt{\frac{64}{315}}\!\,](/w/images/math/d/c/c/dcc8bb284ac4c14428fb6c63b0ddb893.png) |
![\sqrt{\frac{27}{70}}\!\,](/w/images/math/8/a/e/8ae6fd11dfe864b8cb7218eef01f63d9.png) |
![-\sqrt{\frac{32}{105}}\!\,](/w/images/math/a/b/2/ab20b6460dfebf98411536ac0ff4f024.png) |
![\sqrt{\frac{1}{15}}\!\,](/w/images/math/2/f/b/2fb67fa6d0d617d8c5a350c8329a5dbe.png) |
|
SU(N) Clebsch–Gordan coefficients
Algorithms to produce Clebsch–Gordan coefficients for higher values of
and
, 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
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
- ↑ (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.
- ↑ Lua error in package.lua at line 80: module 'strict' not found. Table 1.4 resumes the most common.
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
External links