PX262 - C2c - postulates 2 & 3

every dynamical variable may be represented by a hermitian operator whose eigenvalues represent the possible results of carrying out the measurement of the value of the dynamical variable
immediately after such a measurement, the wavefunction of the system is identical to the eigenfunction corresponding to the eigenvalue obtained as a result of the measurement

the operators representing the position and the momentum of a particle are$\overrightarrow{r}$ and $-i\hslash \overrightarrow{\mathrm{\nabla }}$, respectively
operators reprseneting other dynamical quantities bear the same functional relation to these, as do the corresponding classical quantities to the classical position and momentum variables