- #1
Master J
- 226
- 0
In Sakurai's Modern Quantum Mechanics, he develops the Dirac notation of bras and kets. In one part, he states (page 17):
<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|.
<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|.