By Fourier transform techniques the exact solutions of the one-velocity neutron diffusion problem for a uniform infinite medium with isotropic scattering have been derived for plane isotropic, plane parallel monodirectional, and plane parallel bidirectional source terms. These exact solutions in terms of Fourier inversion integrals were numerically evaluated upon the NAREC to give the angular distribution of the scattered intensity, the total scattered intensity, and the total intensity. By solving the integrals by contour integration in the complex plane, asymptotic solutions were obtained which are good approximate solutions for deep penetrations and problems with little absorption.