Page "Mathematical formulation of quantum mechanics" Paragraph 96

The picture given in the preceding paragraphs is sufficient for description of a completely isolated system.

However, it fails to account for one of the main differences between quantum mechanics and classical mechanics, that is, the effects of measurement.

The von Neumann description of quantum measurement of an observable A, when the system is prepared in a pure state ψ is the following ( note, however, that von Neumann's description dates back to the 1930s and is based on experiments as performed during that time – more specifically the Compton – Simon experiment ; it is not applicable to most present-day measurements within the quantum domain ):