Observable

An observable is a physical quantity that can be measured on a quantum system, such as position, momentum, energy, or spin. In the formalism of quantum mechanics each observable is represented by a linear operator, specifically a self-adjoint operator, acting on the states of the system. The possible results of measuring the observable are exactly the eigenvalues of its operator.

#Measurement outcomes

When an observable is measured, the system yields one of its eigenvalues and is left in the corresponding eigenstate. If the system was not already in an eigenstate, the outcome is probabilistic, with probabilities fixed by the state before measurement. Two observables whose operators do not commute, such as position and momentum, cannot both have definite values at once, a fact expressed by the uncertainty principle. The interpretation of this measurement step is the subject of the measurement problem.