Kalnins, E.G. & Miller, W., Jr. (1985). Differential-Stäckel matrices. Journal of Mathematical Physics, 26, 1560.
Permanent Research Commons link: http://hdl.handle.net/10289/1224
We show that additive separation of variables for linear homogeneous equations of all orders is characterized by differential-Stäckel matrices, generalizations of the classical Stäckel matrices used for multiplicative separation of (second-order) Schrödinger equations and additive separation of Hamilton–Jacobi equations. We work out the principal properties of these matrices and demonstrate that even for second-order Laplace equations additive separation may occur when multiplicative separation does not.
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