Computational determination of wave operators from large Hamiltonian matrices

Abstract

Quantum perturbation theory is reviewed in the framework of wave operators which are ubiquitous from bound states to scattering theory. The wave operators are determined by the iterative solution of non-linear Bloch equations. The convergence properties are improved by means of polynomial approximations of Newton–Raphson factors. Our approach is discussed with respect to other iterative methods. A numerical illustration is presented for two model problems: the determination of low-frequency normal modes in macromolecules and of light-induced resonances in H₂⁺.