Complement to the Wigner-Kirkwood expansion

We extend the region of applicability of phase-space techniques, for the study of quantum systems, by developing an expansion for the Wigner distribution function and correlation functions, in powers of an interaction potential. These results are not restricted to the near-classical regime (expansion in powers of {}), in contrast to the Wigner-Kirkwood expansion. The relation to other perturbation methods (Lindstedt-Poincar\'e, Green's function) is explored.