Quantum state determination: Quorum for a particle in one dimension

In this paper we wish to illuminate the axiom that the quantal state describes a statistical ensemble of similar systems identically prepared, and is not to be identified with any single system. The mathematical representative of the general quantum state is the density matrix or statistical operator in Hilbert space. We demonstrate how this operator may be determined empirically by calculations involving only the measured mean values of a set of observables we call a ’’quorum.’’ As an example of this approach a state determination procedure is described for a spinless particle moving in one dimension; the corresponding quorum turns out to involve only position data associated with various instants subsequent to the act of preparation.