Kalnins, Ernie G.Miller, W., Jr.2008-11-032008-11-031976-03Kalnins, E.G. & Miller, W., Jr. (1976). Lie theory and separation of variables. 9. Orthogonal R-separable coordinate systems for the wave equation ψtt-∆2ψ=0. Journal of Mathematical Physics, 17, 331.0022-2488https://hdl.handle.net/10289/1240A list of orthogonal coordinate systems which permit R-separation of the wave equation ψtt-∆2ψ=0 is presented. All such coordinate systems whose coordinate curves are cyclides or their degenerate forms are given. In each case the coordinates and separation equations are computed. The two basis operators associated with each coordinate system are also presented as symmetric second order operators in the enveloping algebra of the conformal group O(3,2).application/pdfenCopyright 1976 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jspMathematicsJournal Article10.1063/1.522900