PLEASE HELP WITH QUESTION D Question 1a) Starting with the canonical commutations for the position and momentum, work out thefollowing commutators: [Läx], [Lay], [L»,2]. [Lupx]. [Lupy] and [Lz,p=].b) Use these relations to obtained [L,Lx] directly from the classical equation of the angularmomentum.22c) Evaluate the commutators [Lr²] and [L,p²], where ² = x² + y² + z² and p²:= Px + P₂d) Show that H = (p²/2m) + V commute with three components of L provide that V depends onlyon 7.

The Hamiltonian of the system is

a) Starting with the canonical commutations for the position and momentum, work out the following commutators: [Lax], [Lay], [Laz], [La,px], [Lapy] and [L₂pz]. b) Use these relations to obtained [Z,Zx] directly from the classical equation of the angular momentum. c) Evaluate the commutators [L₂,²] and [L,p²], where ² = x² + y² + z² and p² = p² + p²+p². d) Show that H = (p²/2m) + V commute with three components of L provide that V depends only on 7.

a) Starting with the canonical commutations for the position and momentum, work out the following commutators: [Lax], [Lay], [Laz], [La,px], [Lapy] and [L₂pz]. b) Use these relations to obtained [Z,Zx] directly from the classical equation of the angular momentum. c) Evaluate the commutators [L₂,²] and [L,p²], where ² = x² + y² + z² and p² = p² + p²+p². d) Show that H = (p²/2m) + V commute with three components of L provide that V depends only on 7.