This thesis explores finite-size effects on the spin-wave excitations of one-dimensional ferromagnetic and antiferromagnetic systems. Specifically, it presents a theoretical study of the scattering function, the physical observable in inelastic neutron and photon scattering experiments, under the influence of extra magnetic anisotropy energy localized at the system’s boundaries. The method for calculating spin wave scattering functions in bulk is adapted to the finite system case, enabling explicit numerical calculations with edge effects. Our results show a significant broadening of the scattering peaks of low energy spin waves in ferromagnetic and antiferromagnetic systems. We show that broadening is due to the emergence of spin excitations localized at the edge of the system, the so-called edge modes. / Graduate