  It is assumed that the quantum state that may describe a macroscopic system
at a given instant of time is one of the eigenstates of the reduced density
matrix calculated from the wave function of the system plus its environment.
This implies that the above quantum state is a member of a special orthonormed
set of states. Using a suitable Monte-Carlo simulation, this property is shown
to be consistent with the extremely small standard deviation for the
coordinates and the momenta of macroscopic systems. Consequences for
statistical mechanics and possible observable effects are discussed.
