Recursion Method Illustrated

Abstract

The goal of this Chapter is to introduce the non-expert reader to the practicalities of the recursion method and to demonstrate its elegance and aesthetic appeal. All model systems considered in this first round of applications are exactly solvable by one or several methods including the recursion method. We begin with the ultimate overkill of the perennial toy model of physics teachers — the harmonic oscillator. Then we move on to more complex models, but we analyze them only for special situations associated with simple dynamical behavior. The focus here is entirely on the use of calculational techniques. In later Chapters we shall return to some of these same model systems and analyze their complex dynamical properties under more general circumstances.