A constructive solution for a generalized Thomas-Fermi theory of ionized atoms
Authors:
C. Y. Chan and Y. C. Hon
Journal:
Quart. Appl. Math. 45 (1987), 591-599
MSC:
Primary 34B15; Secondary 34B27, 34B30, 81G45
DOI:
https://doi.org/10.1090/qam/910465
MathSciNet review:
910465
Full-text PDF Free Access
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Additional Information
- N. Anderson and A. M. Arthurs, Variational solutions of the Thomas-Fermi equation, Quart. Appl. Math. 39 (1981/82), no. 1, 127–129. MR 613956, DOI https://doi.org/10.1090/S0033-569X-1981-0613956-X
- B. L. Burrows and P. W. Core, A variational-iterative approximate solution of the Thomas-Fermi equation, Quart. Appl. Math. 42 (1984), no. 1, 73–76. MR 736506, DOI https://doi.org/10.1090/S0033-569X-1984-0736506-4
V. Bush and S. H. Caldwell, Thomas–Fermi equation solution by the differential analyzer, Phys. Rev. 38, 1898–1901 (1931)
- C. Y. Chan and S. W. Du, A constructive method for the Thomas-Fermi equation, Quart. Appl. Math. 44 (1986), no. 2, 303–307. MR 856183, DOI https://doi.org/10.1090/S0033-569X-1986-0856183-8
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)
- Herbert B. Keller and Donald S. Cohen, Some positone problems suggested by nonlinear heat generation, J. Math. Mech. 16 (1967), 1361–1376. MR 0213694
- 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, Monotone methods for the Thomas-Fermi equation, Quart. Appl. Math. 36 (1978/79), no. 3, 305–314. MR 508774, DOI https://doi.org/10.1090/S0033-569X-1978-0508774-3
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
R. V. Ramnath, A new analytic approximation for the Thomas–Fermi model in atomic physics, J. Math. Anal. Appl. 31. 285–296 (1970)
- H. L. Royden, Real analysis, 3rd ed., Macmillan Publishing Company, New York, 1988. MR 1013117
A. Sommerfeld, Asymptotische integration der Differential-Gleichung des Thomas–Fermischen Atoms, Z. Phys. 78, 283–308 (1932)
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
N. Anderson and A. M. Arthurs, Variational solutions of the Thomas–Fermi equation, Quart. Appl. Math. 39, 127–129 (1981)
B. L. Burrows and P. W. Core, A variational-iterative approximate solution of the Thomas–Fermi equation, Quart. Appl. Math. 42, 73–76 (1984)
V. Bush and S. H. Caldwell, Thomas–Fermi equation solution by the differential analyzer, Phys. Rev. 38, 1898–1901 (1931)
C. Y. Chan and S. W. Du, A constructive method for the Thomas–Fermi equation, Quart. Appl. Math. 44, 303–307 (1986)
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)
H. B. Keller and D. S. Cohen, Some positone problems suggested by nonlinear heat generation, J. Math. Mech. 16, 1361–1376 (1967)
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, Monotone methods for the Thomas–Fermi equation, Quart. Appl. Math. 36, 305–314 (1978)
M. H. Protter and H. F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1967, p. 6
R. V. Ramnath, A new analytic approximation for the Thomas–Fermi model in atomic physics, J. Math. Anal. Appl. 31. 285–296 (1970)
H. L. Royden, Real analysis, 2nd ed., Macmillan Publishing Co., New York, New York, 1968, p. 88
A. Sommerfeld, Asymptotische integration der Differential-Gleichung des Thomas–Fermischen Atoms, Z. Phys. 78, 283–308 (1932)
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, New York, 1944, pp. 80, 97
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Article copyright:
© Copyright 1987
American Mathematical Society