Compute Commutator: JxJy, Jz | i ħ Result

[nickdi]

Homework Statement

Find the resul of [J_x J_y , J_z] where J is the angular momentum operator.
Possible answers to this multiple chioce question are
A) 0
B) i ħ J_z
C) i ħ J_z J_x
D) i ħ J_x J_z
E) i ħ J_x J_y

Homework Equations

[AB,C]=A [B,C]+[A,B] B
[J_i , J_j]=i ħ ε_ijk J_k where ε_ijk is the Levi-Civita symbol

The Attempt at a Solution

First of all, I used the first formula in this way
[J_x J_y , J_z]=J_x[J_y , J_z]+[J_x , J_z]J_y
Second, I used the second formula to write
J_x[J_y , J_z]+[J_x , J_z]J_y=i ħ(J²_x-J²_y)
Now I am stuck here because this result is not listed in the possible answers.

 

[DuckAmuck]

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

 

[nickdi]

Thanks DuckAmuck for the advice!
That was helpful