On the Perturbation of Boundary Conditions

Abstract

The solution of both the scalar and vector wave equations in regions which are bounded by irregular surfaces which have non-uniform physical properties has been reduced to the solution of a secular equation. The secular determinant is Hermitian. The solution to the secular equation has been expressed in a form suitable for obtaining its value to any approximation. Similar results are given for the corresponding eigenfunctions. Extension of these results to the problem of scattering and to the situation where the bounding surfaces move is indicated. The description of a source located in such a region is also discussed.