PX262 - C10 - the basic postulates

postulate 1

for every dynamical system, there is a wavefunction that is a continuous, square-integrable, single-valued function of the parameters of the system and of time
from this wavefunction, all possible predictions about the physical properties of the system can be obtained

postulate 2

every dynamical variable is represented by a hermitian operator
the measured values correspond to the eigenvalues of the given operator
immediately after the measurement, the wavefunction will be the eigenfunction corresponding to the given eigenvalue

postulate 3

the position and the momentum operators are: $\hat{R} = \vec{r}$ and $\hat{P} = - i ℏ \vec{v}$
the other operators bear the same functional form as in classical physics

postulate 4

when a measurement of a dynamical variable represented by an operator, $\hat{Q}$ , is carried out on a system with a wavefunction, $ψ = \sum_{n} a_{n} ϕ_{n}$ , were $ϕ_{n}$ is an eigenfunction of the operator, then the probability to obtain the result $q_{m}$ will be $| a_{m |^{2}}$

a_{n} = \int ϕ_{n}^{*} ψ d τ

postulate 5

between measurements, the development of the wavefunction is governed by the time-dependent schrödinger equation