Observable

Summary

An observable is a physical quantity of a quantum system that can be measured, such as position, momentum, energy or spin along an axis. In the Hilbert space formulation it is a self-adjoint operator, possibly unbounded, on the Hilbert space of the system. The possible results of a measurement are the points of its spectrum, which is a subset of $\R$. Through the spectral theorem, each observable has a projection-valued measure, which with the state gives the probability of each result.