  An exact-diagonalization technique on small clusters is used to study
low-lying excitations and superconductivity in the two-dimensional negative-$U$
Hubbard model. We first calculate the Bogoliubov-quasiparticle spectrum,
condensation amplitude, and coherence length as functions of the coupling
strength $U/t$, thereby working out how the picture of Bogoliubov
quasiparticles in the BCS superconductors is affected by increasing the
attraction. We then define the Cooper-pair operator as a spatially-extended
composite boson and make a variational evaluation of its internal structure. We
thereby calculate the single-particle spectral function of the Cooper pair and
obtain the dispersion relation for its translational motion. The dynamical
density correlation function of the pairs is also calculated. We thus
demonstrate the applicability of our numerical method for gaining insight into
low-lying excitations of models for the intermediate coupling superconductivity
relevant to cuprate materials.
