What are the expectation values of commutator and anti-commutator for momentum and position operators? In the case of commutator: ⟨[x,p]⟩=⟨iℏ⟩= ?
In the case of anti-commutator: ⟨{x,p}⟩= ?
Answer
iℏ is simply a number, or if you must regard it as an operator, a multiple of the identity. So ⟨iℏ⟩=iℏ, and so is ⟨−iℏ⟩.
By the way, anticommutator of ˆx and ˆp is not [ˆp,ˆx], but {ˆx,ˆp}=ˆxˆp+ˆpˆx.
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