In Sakurai's Modern Quantum Mechanics, he develops the Dirac notation of bras and kets. In one part, he states (page 17):(adsbygoogle = window.adsbygoogle || []).push({});

<B|X|A>

= (<A|X^|B>)*

= <A|X^|B>*

where X^ denotes the Hermitian adjoint (the conjugate transpose) of the operator X.

My question is, since a bra is the conjugate transpose of a ket, could we write

<B|X|A>^ = <A|X|B>

(since of course X^ = X (ie. X is Hermitian) for real, measurable quantities).

What I'm trying to ask is, does Sakurai define a separate conjugate transpose of the bras and kets, whereby he just takes the complex conjugate and implicitly also transposes it (ie.

|A>* = <A| ). Normally, I would expect to see |A>^ = <A|.

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# Dirac notation and conjugate transpose in Sakurai

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