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Adding angular momentum of 2 electrons

  1. Sep 16, 2010 #1
    1. The problem statement, all variables and given/known data

    Use the rules for addition of angular momentum vectors to show that there are 12 possible values of (s',l',j') for two electrons with l1=1, l2=3, s1=1/2, s2=1/2.

    2. Relevant equations

    Total Spin S'=S1 + S2
    Total orbital angular momentum L'=L1 + L2

    Total angular momentum of system J'=L'+S'

    3. The attempt at a solution

    the spin vector S' can have eigenvalues s'=0,1 (I don't know why it just written in the textbook)

    the L' vector apparentely has the rule that l' = abs(l1-l2) .... l1+l2

    so that gives l' = 2, 3, 4

    and apparentely j'= l'+1/2,l'-1/2

    So two j' for each l' means a total of 6 states. Where's the other 6?

    My only thought is that you have to somehow take m_{l} quantum numbers into account but I'm totally confused about that because I don't understand anything about m_{l} quantum numbers.
  2. jcsd
  3. Sep 16, 2010 #2


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    The same rule applies for s', so s' ranges from |1/2-1/2|=0 to 1/2+1/2=1.
    You want to use the values for s', which as you noted above are 0 and 1, not 1/2.
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