Green’s Functions of Classical Particles

Abstract

The simple harmonic oscillator is of importance in different fields of physics. Beside the advantage of a complete analytical treatment this object can be used with benefit to study the conceptual differences between classical physics and Quantum Mechanics, for example. We will come back to this aspect in the last chapter of this book. However, the simple harmonic oscillator is considered in this chapter exclusively from the well-known position of classical physics. Among other things, we will derive the related Green’s function. This will enable us to corroborate some of the aspects addressed from a more general position in the Prologue with first examples. The Green’s function of the simple harmonic oscillator contains as a limiting case the Green’s function of a point mass that moves forceless, on an inclined plane, or that undergoes a free fall. In a next step we consider the Green’s function of the damped harmonic oscillator and study its behaviour if an impressed periodic source is applied. The Green’s function of the damped harmonic oscillator contains the Green’s function of the simple harmonic oscillator and the Green’s function related to the motion of a point mass in the presence of friction as limiting cases.