All effective Hamiltonians fulfilling three very general conditions are derived. It is shown that they all stem both from a transformation operator implicitly defined by a nonlinear equation, and an arbitrary "diagonal" and nonsingular operator. The canonical case is discussed, as well as the particular restrictions that lead to the previous schemes of Bloch, des Cloizeaux, and Jørgensen.

• Received 17 November 1980

DOI:https://doi.org/10.1103/PhysRevA.24.4