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.
N. Anderson, A. M. Arthurs and P. D. Robinson, Nuovo Cimento 57B, 523 (1968)
- Arnold Magowan Arthurs, Complementary variational principles, 2nd ed., The Clarendon Press, Oxford University Press, New York, 1980. Oxford Mathematical Monographs. MR 594935
V. Bush and S. H. Caldwell, Phys. Rev. 38, 1898 (1931)
P. Csavinszky, Phys. Rev. 166, 53 (1968)
- Shigehiro Kobayashi, Some coefficients of the series expansion of the TFD function, J. Phys. Soc. Japan 10 (1955), 824–825. MR 70789, DOI https://doi.org/10.1143/JPSJ.10.824
L. D. Landau and E. M. Lifshitz, Quantum mechanics, Pergamon Press, Oxford, 1958
R. E. Roberts, Phys. Rev. 170, 8 (1968)
N. Anderson, A. M. Arthurs and P. D. Robinson, Nuovo Cimento 57B, 523 (1968)
A. M. Arthurs, Complementary variational principles, Clarendon Press, Oxford, second edition, 1980
V. Bush and S. H. Caldwell, Phys. Rev. 38, 1898 (1931)
P. Csavinszky, Phys. Rev. 166, 53 (1968)
S. Kobayashi, T. Matsukuma, S. Nagai and K. Umeda, J. Phys. Soc. Japan 10, 759 (1955)
L. D. Landau and E. M. Lifshitz, Quantum mechanics, Pergamon Press, Oxford, 1958
R. E. Roberts, Phys. Rev. 170, 8 (1968)
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Article copyright:
© Copyright 1981
American Mathematical Society
