  We explore the relation of Van Vleck-Primas perturbation theory of quantum
mechanics with the Lie-series based perturbation theory of Hamiltonian systems
in classical mechanics. In contrast to previous works on the relation of
quantum and classical perturbation theories, our approach is not based on the
conceptual similarities between the two methods. Instead, we show that for
quantum systems with a finite-dimensional Hilbert space, the Van Vleck-Primas
procedure can be recast exactly into a classical perturbation problem.
