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. For example, 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.
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