Continued Fractions and Upper and Lower Bounds in the Brillouin - Wigner Perturbation Scheme

摘要

A derivation of approximants to a continued fraction development of the energy is presented. It is based on the techniques of infinite order perturbation theory and inner projection of operators. The approximants have been introduced before; here their formal nature is clarified and conditions under which they exhibit extremal properties are presented. The oscillatory behaviour about the true eigenvalue, observed previously in the Mathieu problem, is explained. (Author)