Continued Fraction Expansions in Scattering Theory and Statistical Non-Equilibrium Mechanics

Abstract

We consider several main aspects of the practical application of continued fraction expansions in scattering problems and in the field of equilibrium and non-equilibrium statistical mechanics. We present some recursive algorithms needed for an efficient evaluation of continued fraction coefficients. The method is then applied to the summation of badly converging series which occur in scattering theory and to the asymptotic solution of the Schrödinger equation. In addition, the use of the method for the calculation of response functions, correlations and their derivatives in systems whose time-dependence is described by a master equation is discussed. Finally, the construction of error bounds is investigated.