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

[NewtonApple]

Homework Statement

To show [J², J₊] = 0

2. Homework Equations

J₊ = J_x + i J_y

[J², J_x ] = 0

[J², J_y ] = 0

The Attempt at a Solution

Step 1: L.H.S. = [J², J₊]

Step 2: L.H.S. = [J², J_x + i J_y ]

Step 3: L.H.S. = [J², J_x ] + i [J², J_y ]

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?

 

[Kinta]

Go ahead and write out the full commutator in step 2. What do you get?