Heisenberg picture once more and solving for them with proper initial conditions, leads to Direct computation yields the more general commutator relations, For formula_26, one simply recovers the standard canonical commutation relations valid in all pictures. For a time-independent Hamiltonian "H", Heisenberg picture In physics, the Heisenberg picture (also called the Heisenberg representation) is a formulation (largely due to Werner Heisenberg in 1925) of quantum mechanics in which the operators (observables and others) incorporate a dependency on time, but the state vectors are time-independent, an arbitrary fixed basis rigidly underlying the theory. It stands in contrast to the Schrödinger picture in which
Heisenberg picture line above is the Heisenberg Hamiltonian "H"("t"), which may differ from the Schrödinger Hamiltonian. An important special case of the equation above is obtained if the Hamiltonian does not vary with time. Then the time-evolution operator can be written as Therefore, and, Here ∂"A"/∂"t" is the time derivative of the initial "A", not the "A"("t") operator defined. The last equation holds since commutes with . If the Hamiltonian does not vary with time, then the time-evolution operator can be written as where is the Hamiltonian and is the reduced Planck constant. Therefore, Thus and hence emerges the above Heisenberg equation