Perturbation-iteration methods for large perturbations in quantum mechanics

The introduction of a reduced wave operator X allows us to present in a systematic and transparent way the usual Rayleigh-Schrödinger method. Beyond this scheme and for large perturbations, X is determined by new iterative methods which converge linearly, quadratically or quasi-quadratically. The study of a two-state system exhibits the main characteristics of these methods. The new possibilities afforded by these methods are illustrated by determining the spectrum of the neutral states of a molecule in presence of ionic intruder states.