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what is expectation vaules of commutator and anti commutator when the case is momentum and position. when the case is commutator: $$\langle i\hbar\rangle=?$$ when the case is anti commutator: $$\langle - i\hbar \rangle=?$$

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$i\hbar$ is simply a number, or if you must regard it as an operator, a multiple of the identity. So $\langle i\hbar \rangle=i\hbar$, and so is $\langle -i\hbar \rangle$.

By the way, anticommutator of $\hat{x}$ and $\hat{p}$ is not $[\hat{p},\hat{x}]$, but $\{\hat{x},\hat{p}\}=\hat{x}\hat{p}+\hat{p}\hat{x}$.

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you means that $\langle -i\hbar\rangle=i\hbar$!? – user8784 Jun 16 '12 at 11:32
$\langle -i\hbar\rangle= -i\hbar$. The expectation of any constant is just that constant. – Siyuan Ren Jun 16 '12 at 13:00

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