  We shall present a new strategy for handling mean field limits of quantum
mechanical systems. The new method is simple and effective. It is simple,
because it translates the idea behind the mean field description of a many
particle quantum system directly into a mathematical algorithm. It is effective
because the strategy yields with lesser effort better results than previously
achieved. As an instructional example we treat a simple model for the time
dependent Hartree equation which we derive under more general conditions than
what has been considered so far. Other mean field scalings leading e.g. to the
Gross-Pitaevskii equation can also be treated.
