  We examine the reduced density matrix of the centre of mass on position basis
considering a one-dimensional system of $N$ non-interacting distinguishable
particles in a infinitely deep square potential well. We find a class of pure
states of the system for which the off-diagonal elements of the matrix above go
to zero as $N$ increases. This property holds too for the state vectors which
are factorized in the single particle wave functions. In this last case, if the
average energy of each particle is less than a common bound, the diagonal
elements are distributed according to the normal law with a mean square
deviation which becomes smaller and smaller as $N$ increases towards infinity.
Therefore when the state vectors are of the type considered we cannot
experience spatial superpositions of the centre of mass and we may conclude
that position is a preferred basis for the collective variable.
