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$$\langle m|F|n\rangle^*=\langle F(n)|m\rangle$$ How does the operator become a function of state $|n\rangle$?

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  • $\begingroup$ For <m|F|n>*=<F(n)|m> $\endgroup$ – TA Run Mar 31 '19 at 12:08
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Since $\langle m|F|n\rangle^* = \langle n| F^\dagger |m\rangle$ we can rename the left side into a new bra vector $\langle F(n)| := \langle n | F^\dagger$. There is really no math or physics happening here, only a renaming of terms.

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