None *Problem 4.19(a) Starting with the canonical commutation relations for position and momentum(Equation 4.10), work out the following commutators:[L2, x] = ihy,[Lz, y] = -iħx,[Lz, Px] = ih py, [L2, Py] = -ihp;, [L, Pe] = 0.[L2, z) = 0,[4.122](b) Use these results to obtain [Lz, L;] = iħLy directly from Equation 4.96.(c) Evaluate the commutators [Lz, r*] and [L, p²] (where, of course, r2x² + y? +z? and p² = p;+ p;+ p?).(p²/2m) + V commutes with all three(d) Show that the Hamiltonian Hcomponents of L, provided that V depends only on r. (Thus H, L², and L2are mutually compatible observables.)

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(a) Starting with the canonical commutation relations for position and momentum (Equation 4.10), work out the following commutators: [Lz, y] = -ihx, [L,, z) = 0, [L2, x] = ihy, [L,, p.) = ihpy, [L, Py] = -ihp, [Lz, Pa] = 0, [4.122] (b) Use these results to obtain [Lz, Lx] = ihLy directly from Equation 4.96. (c) Evaluate the commutators [Lz, r²] and [Lz, p²] (where, of course, r2 = x² + y? + z² and p² = p+ p; + p?). %3D

(a) Starting with the canonical commutation relations for position and momentum (Equation 4.10), work out the following commutators: [Lz, y] = -ihx, [L,, z) = 0, [L2, x] = ihy, [L,, p.) = ihpy, [L, Py] = -ihp, [Lz, Pa] = 0, [4.122] (b) Use these results to obtain [Lz, Lx] = ihLy directly from Equation 4.96. (c) Evaluate the commutators [Lz, r²] and [Lz, p²] (where, of course, r2 = x² + y? + z² and p² = p+ p; + p?). %3D