Some aspects on the Bloch-Lindgren equation and a comparison with the partitioning technique

After a brief introduction of the intuitive idea of replacing the ordinary Schrödinger equation with a simpler relation involving a model Hamiltonian and a set of model functions, a strict derivation of the nonlinear form of the Schrödinger equation is given by using a skew-projector Θ associated with two linear subspaces, which justifies this approach. In the case when the Hamiltonian has the form H = Ho + V, the Bloch and Bloch-Lindgren equations are derived, and their solutions in terms of power series in V are discussed. Since the model Hamiltonian does not depend explicitly on the energy E, the attempts to use this approach to build a bridge between the semi-empirical and ab-initio methods in quantum chemistry are briefly reviewed. Finally a comparison of the treatment of similar systems by means of conventional partitioning technique is given, and the problem of the derivation of the wave and reactions operator in a generalized closed form of perturbation theory is discussed. © 1998 Academic Press Inc.