1 Introduction

The Green's function for the wave equation is closely related to the Green's function for the ideal driven harmonic oscillator. Since there is only a single degree of freedom (the oscillator displacement as a function of time) the mathematics is simplified. Further, the Green's function for the driven harmonic oscillator is often covered in undergraduate classical mechanics texts, and everyone has a good physical intuition on what the motion of the oscillator will be during and after a driving force is applied.

Once the harmonic oscillator is understood, the Green's function for the wave equation can be derived by resolving the wave equation into Fourier components, or more generally into the eigenmodes corresponding to the spatial boundary condition. Each mode's equation of motion is identical to a harmonic oscillator. In fact they are often called radiation oscillators in quantum mechanics. Green's theorem then leads to a complete solution.