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Combined system state as product of states

  1. Dec 3, 2012 #1
    Hey,

    I have to express the combined system state of j=5/2, m=5/2 in terms of the products of states j1,m1 and j2,m2.

    [tex]\mid j,m> =\mid\frac{5}{2},\frac{5}{2}>\: ,\: |j_1,m_1> \& |j_2,m_2>[/tex]

    I know that one way of achieving this is for j1=3/2 and j2=1 but I'm not sure how to express this - I think this is involving Clebsch-Gordon coefficients.

    Thanks guys,
    SK
     
  2. jcsd
  3. Dec 3, 2012 #2
    Just from inspecting your J and M, it seems clear a (spin 3/2 with max m=3/2) and a (spin 1/2 with max m=1/2) would combine to that state. As a rule, if your M happens to be the sum of two particular spins' max m, then you have a straightforward product of the states at their max m.
     
  4. Dec 3, 2012 #3
    I suppose I'm confused in how I could write that the 5/2, 5/2 state was the same as 3/2, 3/2 and a 1,1.

    Would this simply be: [tex]|\frac{5}{2},\frac{5}{2}>=|\frac{3}{2},\frac{3}{2}>|1,1>[/tex]

    I'm not really sure what is meant by the product of two states - what notation would be used.
     
  5. Dec 3, 2012 #4
    or

    [tex]|\frac{5}{2},\frac{5}{2}>=|\frac{3}{2},\frac{3}{2},1,1>[/tex]
     
  6. Dec 3, 2012 #5
    I've always used the first one, myself. Not sure about the second.
     
  7. Dec 3, 2012 #6
    Right cool, I thought so to but I'm just a bit confused with my notes - I have two very similar way of writing it. Cheers.
     
  8. Dec 3, 2012 #7
    Also, I should add another condition to my rule above.

    As a rule, if your M happens to be the sum of two particular spins' max m and J=M, then you have a straightforward product of the states at their max m. This holds true if you replace instances of "max" with min" in the previous sentence.
     
  9. Dec 3, 2012 #8
    Indeed, this makes sense. Thanks for the help DocZaius!
     
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