Ch 2.4 The average value of an observable $\hat{A}$ in state $|\psi\rangle$: $\langle\hat{A}\rangle = \langle\psi|\hat{A}|\psi\rangle$. Operationally, it is the mean of many measurements on identically prepared systems. *Common confusion:* The expectation value need not be an eigenvalue. For a spin-