The method of singular eigenfunctions introduced first by Van Kampen and developed later by Case and Mika in connection with a one-velocity transport problem, has been adapted in order to solve the time and energy dependent infinite medium problem. The expansion of neutron density and scattering kernel in series of Hermite functions reduces the Boltzmann equation to a system of homogeneous Hnear equations. The resulting set of regular and singular eigenfunctions is shown to be complete (if w∑nonelastic is assumed to increase monotonically with the neutron velocity w) and explicit formulas are found for the normalization integrals and Green's function.