Symmetry and separation of variables for the Helmholtz and Laplace equations

This paper is one of a series relating the symmetry groups of the principal linear partial differential equations of mathematical physics and the coordinate systems in which variables separate for these equations. In particular, we mention 1 and paper 2 which is a survey of and introduction to the series. Here we apply group-theoretic methods to study the separable coordinate systems for the Helmholtz equation.