- #1
latentcorpse
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pretty simple question. have to prove [itex]\hat{O} \hat{O}\dagger[/itex] is a Hermitian operator.
i found that
[itex]\left( \int \int \int \psi^{\star}(\vec{r}) \hat{O} \hat{O}^{\dagger} \phi(\vec{r}) d \tau \right)^{\star} = \int \int \int \phi^{\star}(\vec{r}) \hat{O}^{\dagger} \hat{O} \phi(\vec{r}) d \tau[/itex]
so all we need to get the result is to establish if the operator commutes with it's hermitian conjugate. I'm guessing it does but don't know why - can someone explain?
i found that
[itex]\left( \int \int \int \psi^{\star}(\vec{r}) \hat{O} \hat{O}^{\dagger} \phi(\vec{r}) d \tau \right)^{\star} = \int \int \int \phi^{\star}(\vec{r}) \hat{O}^{\dagger} \hat{O} \phi(\vec{r}) d \tau[/itex]
so all we need to get the result is to establish if the operator commutes with it's hermitian conjugate. I'm guessing it does but don't know why - can someone explain?