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Combined system state as product of states 
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#1
Dec312, 12:14 PM

P: 209

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 ClebschGordon coefficients. Thanks guys, SK 


#2
Dec312, 12:28 PM

P: 296

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.



#3
Dec312, 12:34 PM

P: 209

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. 


#4
Dec312, 12:35 PM

P: 209

Combined system state as product of states
or
[tex]\frac{5}{2},\frac{5}{2}>=\frac{3}{2},\frac{3}{2},1,1>[/tex] 


#5
Dec312, 01:09 PM

P: 296

I've always used the first one, myself. Not sure about the second.



#6
Dec312, 01:11 PM

P: 209

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.



#7
Dec312, 01:15 PM

P: 296

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. 


#8
Dec312, 04:18 PM

P: 209

Indeed, this makes sense. Thanks for the help DocZaius!



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