  In this work we revise the theory of one electron in a ferromagnetically
saturated local moment system interacting via a Kondo-like exchange
interaction. The complete eigenstates for the finite lattice are derived. It is
then shown, that parts of these states lose their norm in the limit of an
infinite lattice. The correct (scattering) eigenstates are calculated in this
limit. The time-dependent Schr\"odinger equation is solved for arbitrary
initial conditions and the connection to the down-electron Green's function and
the scattering states is worked out. A detailed analysis of the down-electron
decay dynamics is given.
