Observable

In physics, particularly in quantum physics, a system observable is a property of the system state that can be determined by some sequence of physical operations. These operations might involve submitting the system to various electromagnetic fields and eventually reading a value off some gauge. In systems governed by classical mechanics, any experimentally observable value can be shown to be given by a real-valued function on the set of all possible system states. In quantum physics, on the other hand, the relation between system state and the value of an observable is more subtle, requiring some basic linear algebra to explain. In the mathematical formulation of quantum mechanics, states are given by non-zero vectors in a Hilbert space V (where two vectors are considered to specify the same state if, and only if, they are scalar multiples of each other) and observables are given by self-adjoint operators on V. However, as indicated below, not every self-adjoint operator corresponds to a physically meaningful observable. For the case of a system of particles, the space V consists of functions called wave functions.