"The state is normalized" $\to$ $\langle\psi|\psi\rangle = 1$ - $\langle\psi|\hat{H}|\psi\rangle$ $\to$ "the expectation value of energy" $\to$ $\int \psi^* \hat{H}\psi \, dx$ (in position space) - "The probability of measuring $E_n$" $\to$ $|\langle n|\psi\rangle|^2$ $\to$ $\left|\int \psi_n^*\psi