Kalnins, Ernie G.Miller, W., Jr.2008-10-312008-10-311987-05Kalnins, E.G. & Miller, W., Jr. (1987). R-separation of variables for the time-dependent Hamilton–Jacobi and Schrödinger equations. Journal of Mathematical Physics, 28, 1005.0022-2488https://hdl.handle.net/10289/1217The theory of R-separation of variables is developed for the time-dependent Hamilton–Jacobi and Schrödinger equations on a Riemannian manifold V n where time-dependent vector and scalar potentials are permitted. As an application it is shown how to obtain all R-separable coordinates for the n-sphere and Euclidean n-space.application/pdfenCopyright 1987 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.jspMathematicsdifferential equationspartial differential equationsSchroedinger equationHamilton&minusJacobi equationstime dependencemathematical spacemathematical manifoldsanalytical solutionHamiltoniansHamiltonian functioncoordinatespotentialsJournal Article10.1063/1.527592