Please tell me where my understanding of the Heisenberg and/or the Schrodinger picture falls apart. -Schrodinger says the state vector of a system changes with time according to a unitary operator that doesn't change with time. -Hesienberg says the state vector of a system doesn't change with time but the operator acting on that state vector has time dependence. -In the heisenberg equation of motion http://en.wikipedia.org/wiki/Heisenberg_picture , the second term (partial A with respect to t) dissapears (A doesn't change with time) when the Hamiltonian is autonomous. - But if the Hamiltonian is autonomous and we are in the Heisenberg picture then A(t)=A(0) and the system will not evolve with time because the operator A is the only time dependent variable. -However, in the schrodinger picture, the phase of a stationary state can evolve with time. Conclusion: -Therefore, the two pictures do not seem entirely equal.