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Turning a bra made up of a tensor product of two bras into a ket (and vice-versa)

Physics Asked by DJA on November 15, 2020

I know that in general the following statement is true: $$langlephi|chirangle = langlechi|phirangle^* $$

And for the operator $A$ then the following identity also holds:
$$ langle psi| A|phirangle = langlephi|A^dagger |psi rangle$$

Does this mean that (1) implies (2)

$$| psirangle = |chirangle|phirangletag1$$
$$langle psi|= langlephi|langlechi|tag2$$

since I assume$$ langlepsi|psirangle = 1?$$

One Answer

If you are dealing with a composite system as it seems, you don’t need to change the order of $psi$ and $phi$ from (1) to (2), since the first (second) ket/bra always refers to the first (second) subsystem of your larger system. Along the same reasoning, you don’t need to change the order if the two kets/bras refer to two different degrees of freedom of the same system

Correct answer by Milarepa on November 15, 2020

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