ABSTRACT
This chapter employs the following notation and basic formulae of quantum mechanics; the units are such that h = c = 1. Observables are represented in quantum mechanics by Hermitian operators in Hilbert space. These operators are analogues of finite-dimensional Hermitian operators, but the infinite dimensionality requires some mathematical explanation. The physical fact that not all measurements (preparations) are compatible with each other corresponds to the fact that not all operators commute. The ‘state’ of a physical system is fully determined in one way or another if a complete set of compatible measurements has been carried through such that no further measurement exists which is compatible with, and which is not simply a calculable function of, those measurements already made. Since not all independent measurements are compatible, there exist several non-compatible ‘complete sets of measurements’ for a given physical system, which lead to different aspects of that system.
