Computational methods for generalized Thomas-Fermi models of neutral atoms
Authors:
C. Y. Chan and Y. C. Hon
Journal:
Quart. Appl. Math. 46 (1988), 711-726
MSC:
Primary 81G45; Secondary 34A50, 34B15, 34B27, 65L10
DOI:
https://doi.org/10.1090/qam/973385
MathSciNet review:
973385
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
V. Bush and S. H. Caldwall, Thomas-Fermi equation solution by the differential analyzer, Phys. Rev. 38, 1898–1901 (1931)
- C. Y. Chan and Y. C. Hon, A constructive solution for a generalized Thomas-Fermi theory of ionized atoms, Quart. Appl. Math. 45 (1987), no. 3, 591–599. MR 910465, DOI https://doi.org/10.1090/S0033-569X-1987-0910465-4
E. Fermi, Un metodo statistico per la determinazione di alcune proprietá dell’ atomo, Rend. Accad. Naz. del Lincei, Cl. Sci. Fis., Mat. e. Nat. (6) 6, 602–607 (1927)
E. Fermi, Eine statistische Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der Elemente, Z. Phys. 48, 73–79 (1928)
- G. S. Ladde, V. Lakshmikantham, and A. S. Vatsala, Monotone iterative techniques for nonlinear differential equations, Monographs, Advanced Texts and Surveys in Pure and Applied Mathematics, vol. 27, Pitman (Advanced Publishing Program), Boston, MA; distributed by John Wiley & Sons, Inc., New York, 1985. MR 855240
- C. D. Luning, An iterative technique for obtaining solutions of a Thomas-Fermi equation, SIAM J. Math. Anal. 9 (1978), no. 3, 515–523. MR 483486, DOI https://doi.org/10.1137/0509032
- J. W. Mooney, A unified approach to the solution of certain classes of nonlinear boundary value problems using monotone iterations, Nonlinear Anal. 3 (1979), no. 4, 449–465. MR 537330, DOI https://doi.org/10.1016/0362-546X%2879%2990061-0
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
R. E. Roberts, Upper- and lower-bound energy calculations for atoms and molecules in the Thomas-Fermi theory, Phys. Rev. 170, 8–11 (1968)
L. H. Thomas, The calculation of atomic fields, Proc. Cambridge Philos. Soc. 23, 542–548 (1927)
- G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
V. Bush and S. H. Caldwall, Thomas-Fermi equation solution by the differential analyzer, Phys. Rev. 38, 1898–1901 (1931)
C. Y. Chan and Y. C. Hon, A constructive solution for a generalized Thomas-Fermi theory of ionized atoms, Quart. Appl. Math. 45, 591–599 (1987)
E. Fermi, Un metodo statistico per la determinazione di alcune proprietá dell’ atomo, Rend. Accad. Naz. del Lincei, Cl. Sci. Fis., Mat. e. Nat. (6) 6, 602–607 (1927)
E. Fermi, Eine statistische Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der Elemente, Z. Phys. 48, 73–79 (1928)
G. S. Ladde, V. Lakshmikantham, and A. S. Vatsala, Monotone iterative techniques for nonlinear differential equations, Pitman Advanced Publishing Program, Boston, 1985
C. D. Luning, An iterative technique for obtaining solutions of a Thomas–Fermi equation, SIAM J. Math. Anal. 9, 515–523 (1978)
J. W. Mooney, A unified approach to the solution of certain classes of nonlinear boundary value problems using monotone iterations, Nonlinear Anal. 3, 449–465 (1979)
M. H. Protter and H. F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, 1967, p. 6
R. E. Roberts, Upper- and lower-bound energy calculations for atoms and molecules in the Thomas-Fermi theory, Phys. Rev. 170, 8–11 (1968)
L. H. Thomas, The calculation of atomic fields, Proc. Cambridge Philos. Soc. 23, 542–548 (1927)
G. N. Watson, A treatise on the theory of Bessel functions, 2nd ed., Macmillan Co., New York, 1944, pp. 80, 97
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
81G45,
34A50,
34B15,
34B27,
65L10
Retrieve articles in all journals
with MSC:
81G45,
34A50,
34B15,
34B27,
65L10
Additional Information
Article copyright:
© Copyright 1988
American Mathematical Society
