The quasiparticle and spin excitation spectra in the 2D Hubbard model are calculated self-consistently as functions of momentum on the real frequency axis. Near half filling we obtain in the normal state a pseudogap in the density of states. The pairing state has ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry. Below
Tc, gaps open rapidly in the frequency spectra of the gap function, the quasiparticle scattering rate, and the density of states. The scattering rate and spin-lattice relaxation rate drop abruptly below
Tc. Our results are consistent with experiments on ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$.
The one-particle correlation functions of a
dx2-
y2 superconducting state in the two-dimensional Hubbard model are investigated within the fluctuation-exchange approximation. This approximation has been previously applied to investigate properties of the Hubbard-model normal state, including incipient instabilities. Results are obtained for the wave vector and temperature dependence of the one-particle energy gap. A miximum gap ratio 2${\mathrm{\ensuremath{\Delta}}}_{\mathit{k}}^{\mathrm{max}}$(T=0)/
kBTc of order 10 is obtained for intermediate coupling strengths and electron densities near one per site. The potential appearance of spin excitons in two-particle response functions is discussed.