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a) Starting with the canonical commutations for the position and momentum, work out the following commutators: [Lx], [Ly], [Lz], [L₂px]. [Lzpy] and [Läpz]- b) Use these relations to obtained [L,Lx] directly from the classical equation of the angular momentum. c) Evaluate the commutators [L,~²] and [L_,p²], where 7² = x² + y² + z² and p² =p²+p}+p².

a) Starting with the canonical commutations for the position and momentum, work out the following commutators: [Lx], [Ly], [Lz], [L₂px]. [Lzpy] and [Läpz]- b) Use these relations to obtained [L,Lx] directly from the classical equation of the angular momentum. c) Evaluate the commutators [L,~²] and [L_,p²], where 7² = x² + y² + z² and p² =p²+p}+p².

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Question 1 a) Starting with the canonical commutations for the position and momentum, work out the following 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 angular momentum. 2 2 c) Evaluate the commutators [Lr²] and [L,p²], where ² = x² + y² + z² and p²: = Px + P₂ d) Show that H = (p²/2m) + V commute with three components of L provide that V depends only on 7.
Transcribed Image Text:Question 1 a) Starting with the canonical commutations for the position and momentum, work out the following 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 angular momentum. 2 2 c) Evaluate the commutators [Lr²] and [L,p²], where ² = x² + y² + z² and p²: = Px + P₂ d) Show that H = (p²/2m) + V commute with three components of L provide that V depends only on 7.
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