  The Hamiltonian conservative system of two interacting particles has been
considered both in classical and quantum description. The quantum model has
been realized using a symmetrized two-particle basis reordered in the
unperturbed energy. Main attention is paid to the structure of chaotic
eigenfunctions (EF) and to the local spectral density of states (LDOS). A
remarkable correspondence has been found for the shapes of EF and LDOS in the
energy representation, to their classical counterparts. Comparison with the
Band Random Matrix theory predictions has revealed quite significant
differences which are due to dynamical nature of the model. On the other hand,
a partial agreement is found by inserting randomness `` ad hoc '' in the
dynamical model for two-body matrix elements. This shows that, at least for
small number of particles, care must be taken when classical correlations are
neglected. The question of quantum localization in the energy space is
discussed both for dynamical and random model.
