A projector formulation for the Van Vleck transformation

Abstract

The Van Vleck transformation as previously described is generalized so that it can isolate several levels simultaneously. It is shown that the contact transformation involves projectors in an implicit way and that it can be considered as a special case of the generalized Van Vleck transformation. We discuss to what extent the recursion relations (for further transformation of the Nth transform) given in part I can be carried over to the generalized Van Vleck transformation and to the contact transformation. An effective hamiltonian for a particular ‘cluster’ of zeroth-order levels can be obtained in several ways. We compare the results of the usual Van Vleck transformation, Soliverez's transformation and the contact transformation.