  The classical Landau-Lifshitz equation has been derived from quantum
mechanics. Starting point is the assumption of a non-Hermitian Hamilton
operator to take the energy dissipation into account. The corresponding quantum
mechanical time dependent Schr\"odinger, Liouville and Heisenberg equation have
been described and the similarities and differences between classical and
quantum mechanical spin dynamics have been discussed. Furthermore, a time
dependent Schr\"odinger equation corresponding to the classical
Landau-Lifshitz-Gilbert equation and two ways to include temperature into the
quantum mechanical spin dynamics have been proposed.
