Expectation values

qpcrib The expectation value is the “average” value of an observable over very many measurements, and is given by the following for an arbitrary operator $\hat{A}$ in a quantum state $\Psi$

$$<A>=\int {\Psi }^{\ast }(x)\hat{A}\Psi (x)dx$$

This is poorly named, because it is not the most likely value. It is the average value of an observable over all spaces where the wave function can exist.