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GR0177 #43
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Alternate Solutions |
QM320
2008-11-05 20:50:33 | You can also do it by brute force:
![[L_x L_y,L_z] = L_x L_y L_z - L_z L_y L_x](/cgi-bin/mimetex.cgi?[L_x L_y,L_z] = L_x L_y L_z - L_z L_y L_x)
Using the given commutation relations, this is equal to
-(i\hbar L_y+L_x L_z) L_y)
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. :) |  |
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Comments |
QM320
2008-11-05 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
2009-10-23 15:16:39 |
There's a small typo. [LxLy,Lz] = LxLyLz - LzLxLy. Not LxLyLz - LzLyLx as you wrote.
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hybridusmanus
2010-06-15 18:06:16 |
Why can't re-associate the commutations after expansion? rnrni.e. rn[L L ,L ] = rnLLL - LLL =rnL(LL) - (LL)L = rnLihL - ihLL = rnih(L - L )rnrndoes this not always work?
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| | QM320
2008-11-05 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
2008-04-10 14:20:54 | A quick way to do this:
As the commutator is ![[L_xL_y, L_z]](/cgi-bin/mimetex.cgi?[L_xL_y, L_z]) ,
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 +X-Y direction, so thus choice (D) | | bootstrap
2007-04-06 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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