Observable ↩

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created: 2021-12-11 06:48:01
modified: 2022-05-28 14:45:03

In physics, an observable is a physical quantity that can be measured, for example position, momentum, energy, etc. We can define them in quantum mechanics as well as in classical mechanics.

In quantum mechanics

In QM, observables are manifested as Hermitian linear operators on a Hilbert space representing the state of the system (like the wave function). The behavior of the system on measurement is described by the Born rule.

Examples

Position operator

We define the the position operator as multiplying by :

The expectation value is then:

In classical mechanics

In classical mechanics, observables are real-valued functions on the classical phase space canonical coordinates. They are allowed to have explicit time dependence.

Examples

Position and momentum for a particle moving in

For a particle moving in , the classical phase space is , which we think of as pairs . Now the observable for the position of the particle is simply , for the momentum is . and for the energy is .