Observable

Observable

In physics, an observable is a dynamic variable that can be measured. In the context of quantum mechanics, it is a Hermitian operator that can be used to calculate the probabilities of different outcomes of a measurement on a physical system. Observables correspond to the real-valued quantities that define the state of a physical system.

Classical mechanics

In classical mechanics, observables are real-valued functions on the set of all possible system states. Examples of such observables include energy, momentum, angular momentum, and electric charge.

Quantum mechanics

In quantum mechanics, observables are represented by Hermitian operators acting on the Hilbert space associated with the system. The spectrum of values of these operators gives the possible outcomes when the observable is measured. The expectation value of an observable is calculated with respect to the state of the system.

Mathematical formalism

The mathematical formalism of observables in quantum mechanics is a rich subject. It involves the spectral theorem, which connects the properties of a Hermitian operator with the properties of the system it describes. The commutation relations between observables play a crucial role in the structure of quantum mechanics.

See also

• Measurement in quantum mechanics
• Operator (physics)
• Spectral theorem
• Commutation relations