C. Cohen-Tannoudji, B. Diu, F. Laloe, Quanten mechanics 1 & 2

Postulates of QM (preliminary version)
1. The state of a system is described by the wave function ψ(x, t).
| ψ(x, t) | 2 d 3 x = expresses probability of finding the particle at time t at
position x in d 3 x.
2. Quantum mechanically, operators A, B, ... are assigned to the physically measurable
quantities (observables).
3. Average values of operators ψ(x, t) are given by
A = d 3 xψ ∗ (x, t) A ψ(x, t)
4. Time evolution of the states is governed by the Schrödinger equation:
i ∂ ∂t
ψ(x, t) =Hψ(x, t) ; H
= − 2
2m ∇2 + V (x)