assuming \(\ket{\psi}\) is normalized, \(\inp{\psi}=1\). In Dirac notation \(\dyad{a}{b}\) is an operator which when applied to an arbitrary ket \(\ket{\phi}\) yields the ket \(\ket{a}\inpd{b}{\phi}=(\inpd{b}{\phi}) \ket{a}\). The square bracket in \eqref{eqn2} is not standard Dirac notation, but is very convenient and will be used later.