A projector formulation for the Van Vleck transformation

Abstract

A formulation in terms of projection operators of the Van Vleck trans-formation is presented. Explicit formulae through eighth order are given, and the eleventh order may be reached fairly simply. Such high orders are relevant for the Born-Oppenheimer separation. It is proved that the Van Vleck transformation conserves symmetry. A special formulation is given for product spaces. The Foldy-Wouthuysen transformation is treated as an example.