Read the Clebsch-Gordan Coefficients?

[pivoxa15]

How do you read the table?

 

[malawi_glenn]

depends on how it looks like;)

have a look here:

http://www3.tsl.uu.se/thep/courses/QM/061027-exam.pdf

On the last page, in the upper right corner you have the notation.

The big numbers above each (i.e 1/2 x 1/2 ) and so on, are the j_1 and j_2 you want to couple.

This is where CG - coeff comes in:

New = sum over CG x old basis (also called Direct product basis).

i.e

$$| j_1 j_2 ; jm \rangle = \sum _{m_1 m_2} \langle j_1 j_2; m_1 m_2| j_1 j_2 ; m_1 m_2 \rangle | j_1 j_2 ;jm \rangle$$

Where j = j1 + j2
and:
$$\langle j_1 j_2; jm | j_1 j_2 ; m_1 m_2 \rangle$$

Is the CG - coeff.

So the coeff you look up in this table is the ones that enters that sum above.