Operational Solution of Inhomogeneous Wave Equation

Abstract

The Laplace transformation, the three-dimensional Fourier transformation, and the convolution theorem are used to solve the inhomogeneous scalar wave equation in unbounded space. The solutions obtained consist of retarded potential and a function which is expressed as a superposition of the plane wave solutions. The retarded potential solution contains a unit step function which makes the physical explanation of the result more obvious. Some comments on the four-dimensional Fourier transformation method of approach are also included.