Literatur
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H-J=Hamilton-Jacobi.
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This is equivalent to assuming that when the wave equation is separable the same is true of the H-J equation, a statement which can easily be justified on general grounds.
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Madhava Rao, B.S. Separable systems in classical and wave mechanics. Math. Ann. 111, 459–468 (1935). https://doi.org/10.1007/BF01472232
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DOI: https://doi.org/10.1007/BF01472232