  Evidently, physical experiments are practically reproducible even though the
fully identical preparation of initial state wave functions is often far beyond
experimental possibilities. It is thus natural to explore if and in which sense
specific, uncontrollable features of initial wave functions are irrelevant for
the observable course of an experiment. To this end we define ensembles of pure
states which are then shown to generate extremely similar non-equilibrium
dynamics of the expectation values of practically all standard observables. The
ensembles are constructed to comply with some reduced, coarse a priori
information on the state of the system, like, e.g. a few specific expectation
values, etc. However, different types of ensembles with different additional
properties are possible. We discuss some of them.
