  A system of $N$ non-canonical dynamically free 3D harmonic oscillators is
studied. The position and the momentum operators (PM-operators) of the system
do not satisfy the canonical commutation relations (CCRs). Instead they obey
the weaker postulates for the oscillator to be a Wigner quantum system. In
particular the PM-operators fulfil the main postulate, which is due to Wigner:
they satisfy the equations of motion (the Hamiltonian's equations) and the
Heisenberg equations. One of the relevant features is that the coordinate (the
momentum) operators do not commute, but instead their squares do commute. As a
result the space structure of the basis states corresponds to pictures when
each oscillating particle is measured to occupy with equal probability only
finite number of points, typically the eight vertices of a parallelepiped. The
state spaces are finite-dimensional, the spectrum of the energy is finite with
equally spaced energy levels. An essentially new feature is that the angular
momenta of all particles are aligned. Therefore there exists a strong
interaction or correlation between the particles, which is not of dynamical,
but of statistical origin. Another relevant feature is that the standard
deviations of, say, the $k$-th coordinate and the momenta of $\alpha$-th is $
\Delta \hat R_{\alpha k} \Delta \hat P_{\alpha k} \le {p \hbar/{|N-3|}}~(~N\ne
3,~ p -$fixed positive integer), namely instead of uncertainty relations one
has "certainty" relations. The underlying Lie superalgebraic structure of the
oscillator is also relevant and will be explained in the context.
