Gibbs-like ensembles and the inference of pure states

Arguments of the Jaynesʹ maximum entropy sort have proved to be surprisingly successful in providing one with approximate descriptions of pure states in a variety of scenarios, entirely bypassing any consideration of Schrödingerʹs equation. Thus far, however, the concomitant algorithm was unable to incorporate input information concerning expectation values of complementary observables. We discuss here, how to overcome this difficulty by taking recourse to ideas borrowed from Gibbsʹ ones concerning statistical ensembles. The ensuing approach is able to yield, starting from a reduced set of expectation values, approximate wave functions of a rather good quality, as illustrated by simple examples.