1. Starting with the canonical commutation relations for position and momentum [Âi, Âj] = [Îi, Îj] = 0 [Îi‚Âj] = −[Âj, Îi] = −iħdij work out the following commutators, use the definition of Lz below (Q2). [L, x] = iħy, [Ly] = − iħx, [L,z] = 0, [L₂,Px] = iħpy, [L₂,Py] = − iħpx, [L₂Pz] = 0 2. Use these results to obtain [L, Lx] = iħL, directly from - Lx = YPz− ZPy, Ly = zPx − xp₂, L₁ = xPy — YPx 3. Use the results from Q1 to evaluate the commutators [L₂,r²] & [L₂,p²] where: ༡ r² = x² + y² + z² & p² = p²+p²+p² & [L₂,x²] = x[L₂, x] + [L₂, x]x

1. Starting with the canonical commutation relations for position and momentum [Âi, Âj] = [Îi, Îj] = 0 [Îi‚Âj] = −[Âj, Îi] = −iħdij work out the following commutators, use the definition of Lz below (Q2). [L, x] = iħy, [Ly] = − iħx, [L,z] = 0, [L₂,Px] = iħpy, [L₂,Py] = − iħpx, [L₂Pz] = 0 2. Use these results to obtain [L, Lx] = iħL, directly from - Lx = YPz− ZPy, Ly = zPx − xp₂, L₁ = xPy — YPx 3. Use the results from Q1 to evaluate the commutators [L₂,r²] & [L₂,p²] where: ༡ r² = x² + y² + z² & p² = p²+p²+p² & [L₂,x²] = x[L₂, x] + [L₂, x]x