
#1
Jan1413, 02:50 PM

P: 354

Hey!
While I was reading some book in Quantum Mechanics, I ran across the following, and couldn't know how can this be true or actually how was it assumed. How by adding equation (7.91)and (7.92), we get (7.110), see attachment. 



#2
Jan1413, 03:21 PM

P: 123

Well isn't
[tex] \vec{J}=\vec{J}_1+\vec{J}_2 [/tex]? Then you can work component by component and obtain the result. 



#3
Jan1413, 03:53 PM

P: 354

Yes, but this is not the 'real' addition, each of the operators you've listed belong to different spaces..




#4
Jan1413, 04:21 PM

P: 123

Addition of Angular Momenta 



#5
Jan1413, 04:27 PM

P: 354

Please read carefully what's written in the attachment.




#6
Jan1413, 05:32 PM

Sci Advisor
Thanks
P: 3,861

Now if you focus on two of the components, say x and y components, and look at their commutator, [J_{x}, J_{y}] = [J_{1x}, J_{1y}] ⊗ [J_{2x}, J_{2y}] = i J_{1z} ⊗ J_{2z} = i J_{z} 



#7
Jan1513, 02:37 AM

P: 123





#8
Jan1513, 09:48 AM

P: 354

Thanks! This was helpful.



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