We develop the theory of orthogonal R-separation for the Helmholtz equation on a pseudo-Riemannian manifold and show that it, and not ordinary variable separation, is the natural analogy of additive separation for the Hamiltonian-Jacobi equation. We provide a coordinate-free characterization of R-separation in terms of commuting symmetry operators.
Bibliographical noteFunding Information:
One of us (W.M.) would like to thank the University of Waikato for a Postdoctoral Fellowship and kind hospitality which made this collaboration possible.
in part by NSF Grant