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This article is incomplete due to technical limitations.


This is a table of Clebsch-Gordan Coefficients . Another table can be found here (PDF). The overall sign of the coefficients for each set of constant j_1, j_2, j is arbitrary and may go against the convention (that which I have been unable to find).

These are the answers to

  :<math>\langle J 1j 2m 1m 2j 1j 2jm Angle (-1)^{j-j_1-j_2}\langle j_1j_2-m_1,-m_2j_1j_2j,-m angle</math>









J<SUB>1</SUB>=1, J<SUB>2</SUB>=1/2




0, 1/2\sqrt{ rac{2}{3}}\!\,\sqrt{ rac{1}{3}}\!\,



J<SUB>1</SUB>=1, J<SUB>2</SUB>=1




0, 1\sqrt{ rac{1}{2}}\!\,\sqrt{ rac{1}{2}}\!\,


0, 0\sqrt{ rac{2}{3}}\!\,0\!\,-\sqrt{ rac{1}{3}}\!\,
-1, 1\sqrt{ rac{1}{6}}\!\,\sqrt{ rac{1}{2}}\!\,\sqrt{ rac{1}{3}}\!\,



J<SUB>1</SUB>=3/2, J<SUB>2</SUB>=1/2




1/2, 1/2\sqrt{ rac{3}{4}}\!\, rac{1}{2}\!\,


-1/2, 1/2\sqrt{ rac{1}{2}}\!\,\sqrt{ rac{1}{2}}\!\,



J<SUB>1</SUB>=3/2, J<SUB>2</SUB>=1




1/2, 1\sqrt{ rac{3}{5}}\!\,\sqrt{ rac{2}{5}}\!\,


1/2, 0\sqrt{ rac{3}{5}}\!\,-\sqrt{ rac{1}{15}}\!\,-\sqrt{ rac{1}{3}}\!\,
-1/2, 1\sqrt{ rac{3}{10}}\!\,\sqrt{ rac{8}{15}}\!\,\sqrt{ rac{1}{6}}\!\,



J<SUB>1</SUB>=3/2, J<SUB>2</SUB>=3/2




1/2, 3/2\sqrt{ rac{1}{2}}\!\,\sqrt{ rac{1}{2}}\!\,


1/2, 1/2\sqrt{ rac{3}{5}}\!\,0\!\,-\sqrt{ rac{2}{5}}\!\,
-1/2, 3/2\sqrt{ rac{1}{5}}\!\,\sqrt{ rac{1}{2}}\!\,\sqrt{ rac{3}{10}}\!\,


1/2, -1/2\sqrt{ rac{9}{20}}\!\,- rac{1}{2}\!\,-\sqrt{ rac{1}{20}}\!\, rac{1}{2}\!\,
-1/2, 1/2\sqrt{ rac{9}{20}}\!\, rac{1}{2}\!\,-\sqrt{ rac{1}{20}}\!\,- rac{1}{2}\!\,
-3/2, 3/2\sqrt{ rac{1}{20}}\!\, rac{1}{2}\!\,\sqrt{ rac{9}{20}}\!\, rac{1}{2}\!\,



J<SUB>1</SUB>=2, J<SUB>2</SUB>=1/2




1, 1/2\sqrt{ rac{4}{5}}\!\,\sqrt{ rac{1}{5}}\!\,


0, 1/2\sqrt{ rac{3}{5}}\!\,\sqrt{ rac{2}{5}}\!\,



J<SUB>1</SUB>=2, J<SUB>2</SUB>=1




1, 1\sqrt{ rac{2}{3}}\!\,\sqrt{ rac{1}{3}}\!\,


1, 0\sqrt{ rac{8}{15}}\!\,-\sqrt{ rac{1}{6}}\!\,-\sqrt{ rac{3}{10}}\!\,
0, 1\sqrt{ rac{2}{5}}\!\,\sqrt{ rac{1}{2}}\!\,\sqrt{ rac{1}{10}}\!\,


0, 0\sqrt{ rac{3}{5}}\!\,0\!\,-\sqrt{ rac{2}{5}}\!\,
-1, 1\sqrt{ rac{1}{5}}\!\,\sqrt{ rac{1}{2}}\!\,\sqrt{ rac{3}{10}}\!\,



J<SUB>1</SUB>=2, J<SUB>2</SUB>=3/2




1, 3/2\sqrt{ rac{4}{7}}\!\,\sqrt{ rac{3}{7}}\!\,


1, 1/2\sqrt{ rac{4}{7}}\!\,-\sqrt{ rac{1}{35}}\!\,-\sqrt{ rac{2}{5}}\!\,
0, 3/2\sqrt{ rac{2}{7}}\!\,\sqrt{ rac{18}{35}}\!\,\sqrt{ rac{1}{5}}\!\,


1, -1/2\sqrt{ rac{12}{35}}\!\,-\sqrt{ rac{5}{14}}\!\,0\!\,\sqrt{ rac{3}{10}}\!\,
0, 1/2\sqrt{ rac{18}{35}}\!\,\sqrt{ rac{3}{35}}\!\,-\sqrt{ rac{1}{5}}\!\,-\sqrt{ rac{1}{5}}\!\,
-1, 3/2\sqrt{ rac{4}{35}}\!\,\sqrt{ rac{27}{70}}\!\,\sqrt{ rac{2}{5}}\!\,\sqrt{ rac{1}{10}}\!\,



J<SUB>1</SUB>=2, J<SUB>2</SUB>=2




1, 2\sqrt{ rac{1}{2}}\!\,\sqrt{ rac{1}{2}}\!\,


1, 1\sqrt{ rac{4}{7}}\!\,0\!\,-\sqrt{ rac{3}{7}}\!\,
0, 2\sqrt{ rac{3}{14}}\!\,\sqrt{ rac{1}{2}}\!\,\sqrt{ rac{2}{7}}\!\,


1, 0\sqrt{ rac{3}{7}}\!\,-\sqrt{ rac{1}{5}}\!\,-\sqrt{ rac{1}{14}}\!\,\sqrt{ rac{3}{10}}\!\,
0, 1\sqrt{ rac{3}{7}}\!\,\sqrt{ rac{1}{5}}\!\,-\sqrt{ rac{1}{14}}\!\,-\sqrt{ rac{3}{10}}\!\,
-1, 2\sqrt{ rac{1}{14}}\!\,\sqrt{ rac{3}{10}}\!\,\sqrt{ rac{3}{7}}\!\,\sqrt{ rac{1}{5}}\!\,


1, -1\sqrt{ rac{8}{35}}\!\,-\sqrt{ rac{2}{5}}\!\,\sqrt{ rac{1}{14}}\!\,\sqrt{ rac{1}{10}}\!\,-\sqrt{ rac{1}{5}}\!\,
0, 0\sqrt{ rac{18}{35}}\!\,0\!\,-\sqrt{ rac{2}{7}}\!\,0\!\,\sqrt{ rac{1}{5}}\!\,
-1, 1\sqrt{ rac{8}{35}}\!\,\sqrt{ rac{2}{5}}\!\,\sqrt{ rac{1}{14}}\!\,-\sqrt{ rac{1}{10}}\!\,-\sqrt{ rac{1}{5}}\!\,
-2, 2\sqrt{ rac{1}{70}}\!\,\sqrt{ rac{1}{10}}\!\,\sqrt{ rac{2}{7}}\!\,\sqrt{ rac{2}{5}}\!\,\sqrt{ rac{1}{5}}\!\,



J<SUB>1</SUB>=5/2, J<SUB>2</SUB>=1/2




3/2, 1/2\sqrt{ rac{5}{6}}\!\,\sqrt{ rac{1}{6}}\!\,


1/2, 1/2\sqrt{ rac{2}{3}}\!\,\sqrt{ rac{1}{3}}\!\,


-1/2, 1/2\sqrt{ rac{1}{2}}\!\,\sqrt{ rac{1}{2}}\!\,



J<SUB>1</SUB>=5/2, J<SUB>2</SUB>=1




3/2, 1\sqrt{ rac{5}{7}}\!\,\sqrt{ rac{2}{7}}\!\,


3/2, 0\sqrt{ rac{10}{21}}\!\,-\sqrt{ rac{9}{35}}\!\,-\sqrt{ rac{4}{15}}\!\,
1/2, 1\sqrt{ rac{10}{21}}\!\,\sqrt{ rac{16}{35}}\!\,\sqrt{ rac{1}{15}}\!\,


1/2, 0\sqrt{ rac{4}{7}}\!\,-\sqrt{ rac{1}{35}}\!\,-\sqrt{ rac{2}{5}}\!\,
-1/2, 1\sqrt{ rac{2}{7}}\!\,\sqrt{ rac{18}{35}}\!\,\sqrt{ rac{1}{5}}\!\,



J<SUB>1</SUB>=5/2, J<SUB>2</SUB>=3/2




3/2, 3/2\sqrt{ rac{5}{8}}\!\,\sqrt{ rac{3}{8}}\!\,


3/2, 1/2\sqrt{ rac{15}{28}}\!\,-\sqrt{ rac{1}{12}}\!\,-\sqrt{ rac{8}{21}}\!\,
1/2, 3/2\sqrt{ rac{5}{14}}\!\,\sqrt{ rac{1}{2}}\!\,\sqrt{ rac{1}{7}}\!\,


3/2, -1/2\sqrt{ rac{15}{56}}\!\,-\sqrt{ rac{49}{120}}\!\,\sqrt{ rac{1}{42}}\!\,\sqrt{ rac{3}{10}}\!\,
1/2, 1/2\sqrt{ rac{15}{28}}\!\,\sqrt{ rac{1}{60}}\!\,-\sqrt{ rac{25}{84}}\!\,-\sqrt{ rac{3}{20}}\!\,
-1/2, 3/2\sqrt{ rac{5}{28}}\!\,\sqrt{ rac{9}{20}}\!\,\sqrt{ rac{9}{28}}\!\,\sqrt{ rac{1}{20}}\!\,


1/2, -1/2\sqrt{ rac{3}{7}}\!\,-\sqrt{ rac{1}{5}}\!\,-\sqrt{ rac{1}{14}}\!\,\sqrt{ rac{3}{10}}\!\,
-1/2, 1/2\sqrt{ rac{3}{7}}\!\,\sqrt{ rac{1}{5}}\!\,-\sqrt{ rac{1}{14}}\!\,-\sqrt{ rac{3}{10}}\!\,
-3/2, 3/2\sqrt{ rac{1}{14}}\!\,\sqrt{ rac{3}{10}}\!\,\sqrt{ rac{3}{7}}\!\,\sqrt{ rac{1}{5}}\!\,



J<SUB>1</SUB>=5/2, J<SUB>2</SUB>=2




3/2, 2\sqrt{ rac{5}{9}}\!\, rac{2}{3}\!\,


3/2, 1\sqrt{ rac{5}{9}}\!\,-\sqrt{ rac{1}{63}}\!\,-\sqrt{ rac{3}{7}}\!\,
1/2, 2\sqrt{ rac{5}{18}}\!\,\sqrt{ rac{32}{63}}\!\,\sqrt{ rac{3}{14}}\!\,


3/2, 0\sqrt{ rac{5}{14}}\!\,-\sqrt{ rac{2}{7}}\!\,-\sqrt{ rac{1}{70}}\!\,\sqrt{ rac{12}{35}}\!\,
1/2, 1\sqrt{ rac{10}{21}}\!\,\sqrt{ rac{2}{21}}\!\,-\sqrt{ rac{6}{35}}\!\,-\sqrt{ rac{9}{35}}\!\,
-1/2, 2\sqrt{ rac{5}{42}}\!\,\sqrt{ rac{8}{21}}\!\,\sqrt{ rac{27}{70}}\!\,\sqrt{ rac{4}{35}}\!\,


3/2, -1\sqrt{ rac{10}{63}}\!\,-\sqrt{ rac{121}{315}}\!\,\sqrt{ rac{6}{35}}\!\,\sqrt{ rac{2}{105}}\!\,-\sqrt{ rac{4}{15}}\!\,
1/2, 0\sqrt{ rac{10}{21}}\!\,-\sqrt{ rac{4}{105}}\!\,-\sqrt{ rac{8}{35}}\!\,\sqrt{ rac{2}{35}}\!\,\sqrt{ rac{1}{5}}\!\,
-1/2, 1\sqrt{ rac{20}{63}}\!\,\sqrt{ rac{14}{45}}\!\,0\!\,-\sqrt{ rac{5}{21}}\!\,-\sqrt{ rac{2}{15}}\!\,
-3/2, 2\sqrt{ rac{5}{126}}\!\,\sqrt{ rac{64}{315}}\!\,\sqrt{ rac{27}{70}}\!\,\sqrt{ rac{32}{105}}\!\,\sqrt{ rac{1}{15}}\!\,