Some aspects of the convergence behaviour of the Brillouin—Wigner perturbation scheme

Abstract

The notion of the radius of convergence in the context of Brillouin—Wigner perturbation theory is classified with special reference to finite-dimensional problems. A modified procedure is shown to be more useful for infinite-dimensional problems; in particular this demonstrates the role of scaling in assuring convergence for the ground state. Behaviour of the Brillouin—Wigner energy series for the ground state is illustrated by numerically studying the convergence of a model two-by-two matrix perturbation which is beset by the intruder-state problem.