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, was adapted 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 linear equations. The resulting set of regular and singular eigenfunctions is shown to be complete and explicit formulas are found for the normalization integrals and Green's function. (auth)