Answer on Quantum Mechanics Question for joun
must also commute with the third component.
So, [Jz,H]=[[Jx,Jy],H]=[JxJy-JyJx, H]=Jx[Jy,H]+[Jx,H]Jy-Jy[Jx,H]-[Jy,H]Jx=0, because of the "an operator commutes with any two components of J",
We prove that [Jz,H]=0, H - operator
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