ABSTRACT
Chapter 5
Green's Functions
for the Helmholtz Equation
In the previous chapters, we sought solutions to the heat and wave
equations via Green's function. In this chapter, we turn to the reduced
wave equation
r
u+ u = f(r): (5:0:1)
Equation (5.0.1), generally known as Helmholtz's equation, includes the
special case of Poisson's equation when = 0. Poisson's equation has a
special place in the theory of Green's functions because George Green
invented his technique for its solution.
