Abstract
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.
Original language | English (US) |
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Pages (from-to) | 1047-1053 |
Number of pages | 7 |
Journal | Journal of Mathematical Physics |
Volume | 24 |
Issue number | 5 |
DOIs | |
State | Published - 1982 |
Externally published | Yes |