Show [J2, J+] = 0 - Homework Solution

AI Thread Summary
The discussion focuses on proving that the commutator [J2, J+] equals zero. The solution involves breaking down the left-hand side into components using the definitions of J+ and the properties of commutators. It clarifies that since [J2, Jx] and [J2, Jy] both equal zero, the entire expression simplifies to zero. A participant questions the treatment of the imaginary unit 'i' in the commutator, seeking clarification on whether it can be factored out. The thread emphasizes the importance of understanding commutator properties in quantum mechanics.
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Homework Statement



To show [J2, J+] = 0

2. Homework Equations

J+ = Jx + i Jy

[J2, Jx ] = 0

[J2, Jy ] = 0

The Attempt at a Solution



Step 1: L.H.S. = [J2, J+]

Step 2: L.H.S. = [J2, Jx + i Jy ]

Step 3: L.H.S. = [J2, Jx ] + i [J2, Jy ]

Step 4: L.H.S. = 0 + 0

Step 5: L.H.S. = 0

L.H.S. = R.H.S.

I'm kinda confuse about 'Step 3'. Can we take out the 'i' from whole bracket? If yes, then do I have to give any reason for it?
 
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Go ahead and write out the full commutator in step 2. What do you get?
 
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