  We show that eigen-energies and energy eigenstates play different roles in
the equilibration process of an isolated quantum system. Their roles are
revealed numerically by exchanging the eigen-energies between an integrable
model and a non-integrable model. We ?find that the structure of eigenenergies
of a non-integrable model characterized by non-degeneracy ensures that quantum
revival occurs rarely whereas the energy eigenstates of a non-integrable model
suppress the fluctuations for the equilibrated quantum state. Our study is
aided with a quantum entropy that describes how randomly a wave function is
distributed in quantum phase space. We also demonstrate with this quantum
entropy the validity of Berry's conjecture for energy eigenstates. This implies
that the energy eigenstates of a non-integrable model appear indeed "random".
