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Operators and observables
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Measurable quantities are represented by Hermitian operators.
Each observable (position, momentum, energy) is a Hermitian operator; measured values are its eigenvalues. Momentum p̂ = −iħ ∂/∂x.
Energy operator Ĥ = p̂²/2m + V.
Measuring gives one eigenvalue, never the average.
In more detail
In quantum mechanics, measurable quantities are represented by operators acting on wavefunctions. Their eigenvalues are the possible measurement results.
Real-world uses
- Energy, momentum and position are represented by operators in calculations.
- Quantum software uses operators to define measurements.
- Quantum engineers represent measurable properties such as energy and spin as operators acting on states.
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Frequently asked questions
What is an eigenvalue?
A value that an operator gives when applied to a state, and it is a possible measurement result.
Are all operators observables?
Observables are Hermitian operators, which give real eigenvalues.
Why are observables Hermitian operators?
Hermitian operators have real eigenvalues, which correspond to the measurable values of the observable.
Related topics in Quantum Mechanics
Normalisation · Schrödinger equation (time-dependent) · Schrödinger equation (time-independent) · Commutators · Particle in a box · Free particle