The slowing down of fast neutrons was analyzed by a multi-group method of discrete time and energy states coupled with a spatial harmonic expansion method to determine the neutron density in a homogeneous, isotropically scattering slab. Five neutron source geometries were studied for both a fissioning and a non-fissioning system. Numerical results were obtained for the neutron flux, mean neutron energy and the neutron spectra for the one dimensional system using a harmonic mode expansion of up to six terms to determine the time-energy-space dependence. (Author).