ABSTRACT
This chapter shows an eigenfunction expansion for a Green’s function for a specific geometry. The eigenfunction expansion can be obtained by substituting the corresponding form for the reduced Green’s function. The Bessel function of zeroth order is introduced upon performing angular integration. A complete eigenfunction decomposition could be obtained by using an addition theorem, and a new type of Bessel function, the modified Bessel function of zeroth order defined by the integral representation, is encountered. The parallel conducting plates suppress most effectively the Coulomb field of the point charge at large distances, on the scale set by a specific distance. That is qualitatively clear in the picture wherein the conductors are replaced by the infinite set of image charges; the potentials of the two lattices composed of positive and negative charges, respectively, will cancel almost completely at large distances.
