Heisenberg picture

Summary

The Heisenberg picture is the way of describing quantum dynamics in which observables change in time and state vectors stay fixed. An observable $A$ becomes $A(t) = U(t)^* A\, U(t)$, where $U(t) = e^{-itH/\hbar}$ is generated by the Hamiltonian. It gives the same expectation values as the Schrödinger picture. Its equation of motion $\frac{d}{dt}A(t) = \frac{i}{\hbar}[H, A(t)]$ has the same form as Hamilton's equations written with the Poisson bracket, which makes the link with classical mechanics clear.