# Compute a commutator

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1. Sep 23, 2016

### nickdi

1. The problem statement, all variables and given/known data
Find the resul of [Jx Jy , Jz] where J is the angular momentum operator.
Possible answers to this multiple chioce question are
A) 0
B) i ħ Jz
C) i ħ Jz Jx
D) i ħ Jx Jz
E) i ħ Jx Jy

2. Relevant equations
[AB,C]=A [B,C]+[A,B] B
[Ji , Jj]=i ħ εijk Jk where εijk is the Levi-Civita symbol

3. The attempt at a solution
First of all, I used the first formula in this way
[Jx Jy , Jz]=Jx[Jy , Jz]+[Jx , Jz]Jy
Second, I used the second formula to write
Jx[Jy , Jz]+[Jx , Jz]Jy=i ħ(J2x-J2y)
Now I am stuck here because this result is not listed in the possible answers.

Last edited: Sep 23, 2016
2. Sep 23, 2016

### DuckAmuck

Your math is fine. Just remember that within those J's are pauli spin matrices. When those are squared they equal 1.

3. Sep 23, 2016