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[tex]

\langle\beta|\cdot\left(X|\alpha\rangle\right) = \left(\langle\beta|X\right)\cdot|\alpha\rangle

[/tex]

so we might as well write [tex]\langle\beta|X|\alpha\rangle[/tex]. I know this is basic stuff, but I thought this notation only made sense when X is hermitian since when you let X act on the bra instead of the ket you must take the hermitian conjugate. Like this:

[tex]

\langle\beta|\cdot\left(X|\alpha\rangle\right) = \left(\langle\beta|X^\dagger\right)\cdot|\alpha\rangle

[/tex]

It's pretty bad that I'm in trouble already in the first chapter (exam next thursday).