Using dynamical density functional theory (DDFT), we theoretically study Brownian self-diffusion and structural relaxation of hard disks and compare to experimental results on quasi two-dimensional colloidal hard spheres. To this end, we calculate the self and distinct van Hove correlation functions by extending a recently proposed DDFT-approach for three-dimensional systems to two dimensions. We find that the theoretical results for both self- and distinct part of the van Hove function are in very good quantitative agreement with the experiments up to relatively high fluid packing fractions of roughly 0.60. However, at even higher densities, deviations between experiment and the theoretical approach become clearly visible. Upon increasing packing fraction, in experiments the short-time self diffusive behavior is strongly affected by hydrodynamic effects and leads to a significant decrease in the respective mean-squared displacement. In contrast, and in accordance with previous simulation studies, the present DDFT which neglects hydrodynamic effects, shows no dependence on the particle density for this quantity
