For an opeation as follow(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\langle \varphi | \hat{A} |\psi\rangle[/tex]

where [tex]\hat{A}[/tex] is an operator.

It is no problem to have [tex]\hat{A}[/tex] directly operate on the ket state [tex]|\psi\rangle[/tex], but if I want [tex]\hat{A}[/tex] operates on the bra state [tex]\langle\varphi |[/tex], do I have to take the adjoint of A first? That is

[tex]\left(\langle \varphi | \hat{A}^\dagger\right) |\psi\rangle = \langle \varphi | \left(\hat{A} |\psi\rangle\right)[/tex]

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# Adjoint operator

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