Combinatorical analysis of the Rayleigh–Schrödinger perturbation theory based on a circular scale of time

Abstract

AbstractContractions of events examined on a circular scale of time have been applied to combinatorical analysis of the Rayleigh–Schrödinger (RS) perturbation theory. The main practical aim of the analysis was to split any of the RS perturbation terms for energy belonging to an order N into product of RS energy terms belonging to perturbation orders N′, N″, N‴ … lower than N. Solely the perturbation of a nondegenerate state is examined. The analysis is illustrated by the whole ensemble of the RS perturbation terms entering the perturbation orders N = 8, 9, and 10 taken as examples. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004