The isotropic form of the classical space-dependent neutron slowing down problem is solved by applying a Fourier transform with respect to optical distance to the appropriate transport equation and boundary conditions. An analytical solution, step-by-step with respect to the “relative” lethargy, is constructed in the transform space; the inversion is facilitated by the use of Bromwich’s technique. In the process, a procedure for determining the lethargy-dependent spatial moments of the total (scalar) flux is developed.