We study the effects of microscopic scattering processes, such as carrier-LA phonon scattering and carrier-carrier Coulomb scattering, on the intraband relaxation dynamics and optical properties of the electron-hole system of a quantum wire. We assume a low excitation density and a low carrier density. In this case, carrier-LA phonon scattering and carrier-carrier Coulomb scattering are both important for relaxation dynamics. Relaxation dynamics are investigated using a full-quantum-mechanical formulation, which is based on semiconductor luminescence equations and a projection-operator theory. In this paper, the time-resolved photoluminescence dynamics can be calculated because the light field is quantized. We reveal the connection between the microscopic scattering and macroscopic relaxation processes. Furthermore, although the microscopic motion of carriers cannot be observed directly in experiments, we can estimate such motion by time-resolved optical spectroscopy.