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Lie theory and the wave equation in space–time. 4. The Klein–Gordon equation and the Poincaré group
A detailed classification is made of all orthogonal coordinate systems for which the Klein–Gordon equation in space–time, tt−3=, admits a separation of variables. We show that the Kl...
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Lie theory and the wave equation in space–time. 5. R-separable solutions of the wave equation psitt−Delta3psi=0

J. Math. Phys. 19, 1247 (1978); doi:10.1063/1.523820

Issue Date: June 1978

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E. G. Kalnins and W. Miller, Jr.
Department of Mathematics, University of Waikato, Hamilton, New Zealand
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
A detailed classification is made of all orthogonal coordinate systems for which the wave equation psitt−Delta3psi=0 admits an R-separable solution. Only those coordinate systems are given which are not conformally equivalent to coordinate systems that have already been found in previous articles. We find 106 coordinates to given a total of 368 conformally inequivalent orthogonal coordinates for which the wave equation admits an R separation of variables. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.
Permalink: http://link.aip.org/link/?JMAPAQ/19/1247/1
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PACS

  • 03.65.Ge
    Classical and quantum physics; mechanics and fields Quantum theory; quantum mechanics Solutions of wave equations: bound states
  • 03.65.Fd
    Classical and quantum physics; mechanics and fields Quantum theory; quantum mechanics Algebraic methods
  • 02.20.Qs
    Mathematical methods in physics Group theory General properties, structure, and representation of Lie groups
  • YEAR: 1978

PUBLICATION DATA

ISSN:
0022-2488 (print)   1089-7658 (online)
Publisher:
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REFERENCES (9)
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  1. E. G. Kalnins and W. Miller, Jr., “Lie theory and the wave equation in space-time. 1. The Lorentz group,” J. Math. Phys. 18, 1 (1977).
  2. E. G. Kalnins and W. Miller, Jr., “Lie theory and the wave equation in space-time. 2. The group SO(4,C),” SIAM J. Math. Anal. (to appear).
  3. E. G. Kalnins and W. Miller, Jr., “Lie theory and the wave equation in space-time. 3. Semisubgroup coordinates,” J. Math. Phys. 18, 271 (1977).
  4. E. G. Kalnins and W. Miller, Jr., “Lie theory and the wave equation in space-time. 4. The Klein-Gordon equation and the Poincare group,” J. Math. Phys. 19, 1233 (1978).
  5. E. G. Kalnins and W. Miller, Jr., “Lie theory and separation of variables and orthogonal R-separable coordinate systems for the wave equation Psitt−Delta2Psi = 0,” J. Math. Phys. 17, 331 (1976).
  6. M. Bocher, Ueber die Reihenentwickelungen der Potentialtheorie (Teubner, Leipzig, 1894).
  7. E. G. Kalnins, W. Miller, and P. Wintenitz, “The group 0(4), separation of variables, and the Hydrogen atom,” SIAM J. Appl. Math. (to appear).
  8. M. P. Olevski, Mat. Sbornik. 27, 379 (1950).
  9. P. Winternitz, I. Lukac, and Ya. A. Smorodinski, “Quantum numbers of the Little groups of the Poincare group,” Sov. J. Nucl. Phys. 7, 139 (1968).

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