Ch 6.4 An operator satisfying $\hat{A}^\dagger = \hat{A}$. Equivalently, $\langle\phi|\hat{A}|\psi\rangle = \langle\hat{A}\phi|\psi\rangle$ for all states. Hermitian operators have real eigenvalues and orthogonal eigenstates. All physical observables are represented by Hermitian operators. *See also