The time evolution operaton may be written formally as: This is an actual solution to: only in the case that [H(t1),H(t2)]=0 (that is: the hamiltonian commutes in different instants of time) Of course, this includes the case of a time independent hamiltonian. If this is not the case, the actual U(t) may be obtained with the Dyson series. This is what is stated in Sakurai, for example. But I don't really understand WHY you cannot use the exponential form of U(t) in case the Hamiltonian doesn't commute at different times. I guess it may have something to do with its integrability, but I don't know. Any hints?