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Read the Clebsch-Gordan Coefficients?

  1. Oct 13, 2007 #1
    How do you read the table?
     
  2. jcsd
  3. Oct 13, 2007 #2

    malawi_glenn

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    depends on how it looks like;)

    have a look here:

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

    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

    [tex] | 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 [/tex]

    Where j = j1 + j2
    and:
    [tex]\langle j_1 j_2; jm | j_1 j_2 ; m_1 m_2 \rangle [/tex]

    Is the CG - coeff.

    So the coeff you look up in this table is the ones that enters that sum above.
     
    Last edited by a moderator: May 3, 2017
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