The exact solution for the Peierls-Heisenberg antiferromagnetic (AF) model in a finite cluster is presented. The spin-spin coupling is retained up to second neighbours. The quantum mechanical character of the phonon variables is maintained in order to properly describe the fluctuations, which have a substantial role in one dimension. The problem of the frustrated AF state is briefly addressed. For the purpose of comparison, Born-Oppenheimer (BO) calculations are also provided. A noticeable result is the fact that the (semiclassical) BO approximation overestimates quantum fluctuations.