Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Variational solutions of the Thomas-Fermi equation


Authors: N. Anderson and A. M. Arthurs
Journal: Quart. Appl. Math. 39 (1981), 127-129
MSC: Primary 81C05; Secondary 49H05, 81G45
DOI: https://doi.org/10.1090/qam/613956
MathSciNet review: 613956
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Abstract: Variational solutions of the Thomas-Fermi equation are examined in the context of complementary extremum principles. A new one-parameter trial function is found to provide an accurate representation of the solution.


References [Enhancements On Off] (What's this?)

  • [1] N. Anderson, A. M. Arthurs and P. D. Robinson, Nuovo Cimento 57B, 523 (1968)
  • [2] Arnold Magowan Arthurs, Complementary variational principles, 2nd ed., The Clarendon Press, Oxford University Press, New York, 1980. Oxford Mathematical Monographs. MR 594935
  • [3] V. Bush and S. H. Caldwell, Phys. Rev. 38, 1898 (1931)
  • [4] P. Csavinszky, Phys. Rev. 166, 53 (1968)
  • [5] Shigehiro Kobayashi, Some coefficients of the series expansion of the TFD function, J. Phys. Soc. Japan 10 (1955), 824–825. MR 0070789, https://doi.org/10.1143/JPSJ.10.824
  • [6] L. D. Landau and E. M. Lifshitz, Quantum mechanics, Pergamon Press, Oxford, 1958
  • [7] R. E. Roberts, Phys. Rev. 170, 8 (1968)

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DOI: https://doi.org/10.1090/qam/613956
Article copyright: © Copyright 1981 American Mathematical Society


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