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2. Angular momentum commutators a) Show that [L2, L] = 0. Hint: calculate [L2x L:] by adding and subtracting LxLzLx and -LxLzLx, and similarly for [L2y,Lz]. b) Defining L plus minus = Lx plus minus iLk, show that L2 = L + L _ + L 2z - Lz = L_L + L2z + Lz. c) Show that [H, L2] and [H, Lz] are both zero. Hint: use Griffiths Eq. (4.129) and (4.132) for Lz and L2 to simply the proof.

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