Compute Commutator: JxJy, Jz | i ħ Result

In summary, when finding the result of [Jx Jy , Jz] where J is the angular momentum operator, the possible answers are A) 0, B) i ħ Jz, C) i ħ Jz Jx, D) i ħ Jx Jz, and E) i ħ Jx Jy. Using the formula [AB,C]=A [B,C]+[A,B] B and [Ji , Jj]=i ħ εijk Jk, the solution is i ħ(J2x-J2y), which is not listed in the possible answers due to the pauli spin matrices within the J's being squared and equaling 1
  • #1
nickdi
2
0

Homework Statement


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

Homework Equations


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

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:
Physics news on Phys.org
  • #2
Your math is fine. Just remember that within those J's are pauli spin matrices. When those are squared they equal 1.
 
  • Like
Likes nickdi
  • #3
Thanks DuckAmuck for the advice!
That was helpful
 

What is the commutator of Jx and Jy?

The commutator of Jx and Jy is given by [Jx, Jy] = iħJz, where i is the imaginary unit and ħ is the reduced Planck constant.

What is the commutator of Jz with itself?

The commutator of Jz with itself is zero, as [Jz, Jz] = JzJz - JzJz = 0.

What is the physical significance of the commutator in quantum mechanics?

The commutator provides a measure of the non-commutativity of two quantum operators. In quantum mechanics, the order in which operators are applied matters, and the commutator quantifies the degree to which the operators do not commute.

How do you compute the commutator of two operators?

The commutator of two operators A and B is given by [A, B] = AB - BA. To compute the commutator of Jx and Jy, we would multiply Jx by Jy and subtract Jy multiplied by Jx.

What is the significance of the commutator in spin measurements?

In spin measurements, the commutator of two spin operators gives the uncertainty in the measurement of the two operators. This is known as the Heisenberg uncertainty principle, which states that the product of the uncertainties in two non-commuting operators cannot be smaller than a certain limit, given by ħ/2.

Similar threads

  • Advanced Physics Homework Help
Replies
3
Views
3K
  • Advanced Physics Homework Help
Replies
3
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
8
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
5
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
4
Views
9K
  • Advanced Physics Homework Help
Replies
2
Views
7K
  • Advanced Physics Homework Help
Replies
14
Views
2K
Back
Top