Time-Dependent Equations of Motion

In Chap.  7 , we derived the time-dependent Schrödinger equation from the properties of time translations applied to the system states. With this approach, the time evolutionTime evolution of the average values of physical variables in non-stationary conditions can be determined from the time evolution of states. An alternative approach is the so-called Heisenberg representation: the time evolution can be studied by applying the corresponding unitary operator \(\textbf{U}(t,t')\) to the observables, rather than the states.