Arguments of the Jaynes maximum entropy sort have proved to be surpris
ingly successful in providing one with approximate descriptions of pur
e states in a variety of scenarios, entirely bypassing any considerati
on of Schrodinger's equation. Thus far, however, the algorithm has bee
n unable to incorporate input information concerning expectation value
s of complementary observables. We discuss here how to overcome this d
ifficulty by recourse to diagonal hypervirial theorems.