In physics, the Heisenberg picture is a formulation of quantum mechanics in which the operators (observables and others) incorporate a dependency on time, but the state vectors are time-independent. It stands in contrast to the Schrödinger picture in which the operators are constant and the states evolve in time. The two models only differ by a basis change with respect to time-dependency, which is the difference between active and passive transformation. The Heisenberg picture is the formulation of matrix mechanics in an arbitrary basis, in which the Hamiltonian is not necessarily diagonal.
In the Heisenberg picture of quantum mechanics the state vector, Failed to parse (Missing texvc executable; please see math/README to configure.): |\psi \rang , does not change with time, and an observable A satisfies
where H is the Hamiltonian and [·,·] is the commutator of A and H. In some sense, the Heisenberg picture is more natural and fundamental than the Schrödinger picture, especially for relativistic theories. Lorentz invariance is manifest in the Heisenberg picture.
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