Kalnins, E.G. & Miller, W., Jr. (1983). The general theory of R-separation for Helmholtz equations. Journal of Mathematical Physics, 24, 1047.
Permanent Research Commons link: https://hdl.handle.net/10289/1227
We develop the theory of R-separation for the Helmholtz equation on a pseudo-Riemannian manifold (including the possibility of null coordinates) and show that it, and not ordinary variable separation, is the natural analogy of additive separation for the Hamilton–Jacobi equation. We provide a coordinate-free characterization of variable separation in terms of commuting symmetry operators.
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