- #1
Andrusko
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Homework Statement
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.
Homework Equations
Total Spin S'=S1 + S2
Total orbital angular momentum L'=L1 + L2
Total angular momentum of system J'=L'+S'
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.