We have examined numerical calculations on a spin 1/2 one‐dimensional (1D) Heisenberg antiferromagnet for N=8 spins, both for the states and their spectral weights. This work is of interest because of the recent neutron scattering experiments in CuCl 2⋅2NC5D5 which show the spectral weight to be concentrated at the des Cloizeaux and Pearson (dCP) spin wave frequencies. The states form a two‐parameter continuum between the dCp value E 1(k) =π‖J‖ ‖sin k‖ and the upper limit E 2(k) =2π‖J‖ ‖ sin(k/2) ‖. Though most of the spectral weight is at the dCP frequency for N=8, about 10% of it is found near E 2 for k=π. There is no numerical evidence for the existence of singlet bound states as predicted by Ovchinnikov.