Ch 6.4 The adjoint of an operator $\hat{A}$, written $\hat{A}^\dagger$, is defined by $\langle\phi|\hat{A}^\dagger|\psi\rangle = \langle\psi|\hat{A}|\phi\rangle^*$ for all states $|\phi\rangle$, $|\psi\rangle$. For a matrix representation, $A^\dagger = (A^T)^*$ (transpose and complex conjugate). An