GR0177 #43



Alternate Solutions 
QM320 20081105 20:50:33  You can also do it by brute force:
Using the given commutation relations, this is equal to
Rearranging and canceling gives choice (D).
Note: This was supposed to be an alternate solution, so I've reposted it as such. If someone could tell me how to delete my original (duplicate) comment, below, that would be helpful. :)  

Comments 
QM320 20081105 20:50:33  You can also do it by brute force:
Using the given commutation relations, this is equal to
Rearranging and canceling gives choice (D).
Note: This was supposed to be an alternate solution, so I've reposted it as such. If someone could tell me how to delete my original (duplicate) comment, below, that would be helpful. :)
thisguy 20091023 15:16:39 
There's a small typo. [LxLy,Lz] = LxLyLz  LzLxLy. Not LxLyLz  LzLyLx as you wrote.

hybridusmanus 20100615 18:06:16 
Why can't reassociate the commutations after expansion? rnrni.e. rn[LL,L] = rnLLL  LLL =rnL(LL)  (LL)L = rnLihL  ihLL = rnih(L  L)rnrndoes this not always work?

walczyk 20110407 08:51:16 
Just wanted to clarify what the typo was and why it is significant. We cannot commute these orbital momentum operators willy nilly, without adding extra terms and whatnot so its a delicate procedure you could say. So beginning we have . Let's follow the original approach and try to substitute something for and . Quickly write out , rearrange to get . You can keep going with it if you'd like.
I'm curious what happens if you try to do something different.. , so we've got .

  QM320 20081105 20:49:13  You can also do it by brute force:
Using the given commutation relations, this is equal to
Rearranging and canceling gives choice (D).   Anastomosis 20080410 14:20:54  A quick way to do this:
As the commutator is ,
Use the right hand rule to point first in the +X+Y (diagonal) direction, and then curl up to the Z direction. Your thumb will be pointing in the +XY direction, so thus choice (D)   bootstrap 20070406 20:15:33  The question have it setup as [AB,C] which is [AB,C] = A[B,C] + [A,C]B. Its very similar to what is posted..  

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