(a) Starting with the canonical commutation relations for position and momentum (Equation...

(a) Starting with the canonical commutation relations for position and momentum (Equation 4.10), work out the following commutators:

 [4.122]

(b) Use these results to obtain [Lz, Lv] = ihLy directly from Equation 4.96.

(c) Evaluate the commutators [Lz, r2] and [Lz, p2] (where, of course, r2 = x2 + y2 + z2 and p2 = +  +).

(d) Show that the Hamiltonian H = (p2/2m) + V commutes with all three components of L, provided that V depends only on r. (Thus H, L2, and Lz are mutually compatible observables.)