Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

An iterative technique for solution of the Thomas-Fermi equation utilizing a nonlinear eigenvalue problem


Authors: C. D. Luning and W. L. Perry
Journal: Quart. Appl. Math. 35 (1977), 257-268
MSC: Primary 34B25; Secondary 81.34
DOI: https://doi.org/10.1090/qam/445056
MathSciNet review: 445056
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Development of an iterative solution technique for a certain nonlinear eigenvalue problem supplies an iterative solution technique for the ion case and isolated neutral atom case boundary-value problems for the Thomas-Fermi equation.


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

  • [1] L. H. Thomas, The calculation of atomic fields, Proc. Camb. Phil. Soc. 23, 542-548 (1927)
  • [2] E. Fermi, Un metodo statistico par la determinazione di alcune proprietá dell' atome, Rend. Accad. Naz. del Lincei. CI. sci. fis., mat. e nat. (6) 6, 602-607 (1927)
  • [3] P. Csavinszky, Calculation of diamagnetic susceptibilities of ions using a universal approximate analytical solution of the Thomas-Fermi equation, Bull. Amer. Phys. Soc. (2) 18, 726-727 (1973)
  • [4] P. Csavinszky, Universal approximate analytical solution of the Thomas-Fermi equation for ions, Phys. Rev. A(3) 8, 1688-1701 (1973)
  • [5] Y. Bae Suh, Perturbation calculation using Thomas-Fermi model, Phys. Lett. 49A, 99-100 (1974)
  • [6] E. H. Lieb and B. Simon, Thomas-Fermi theory revisited, Phys. Rev. Lett. 31, 681-683 (1973)
  • [7] Elliott H. Lieb and Barry Simon, The Thomas-Fermi theory of atoms, molecules and solids, Advances in Math. 23 (1977), no. 1, 22–116. MR 0428944, https://doi.org/10.1016/0001-8708(77)90108-6
  • [8] P. Gombás, Die statistische Theorie des Atoms, Springer, Berlin, 1949
  • [9] N. H. March, The Thomas-Fermi approximation in quantum mechanics, Adv. Phys. 6, 1-101 (1957)
  • [10] James S. W. Wong, On the generalized Emden-Fowler equation, SIAM Rev. 17 (1975), 339–360. MR 0367368, https://doi.org/10.1137/1017036
  • [11] E. B. Baker, The application of the Thomas-Fermi statistical model to the calculation of potential distribution of positive ions, Phys. Rev. 36, 630-647 (1930)
  • [12] A. Sommerfeld, Asymptotische Integration der Differential-Gleichung des Thomas-Fermischen Atoms, Z. Phys. 78, 283-308 (1932)
  • [13] Harold T. Davis, Introduction to nonlinear differential and integral equations, Dover Publications, Inc., New York, 1962. MR 0181773
  • [14] V. Bush and S. H. Caldwell, Thomas-Fermi equation solution by the differential analyzer, Phys. Rev. (2) 38, 1898-1901 (1931)
  • [15] R. V. Ramnath, A new analytical approximation for the Thomas-Fermi model in atomic physics, J. Math. Anal. Appl. 31, 285-296 (1970)
  • [16] R. P. Feynman, N. Metropolis, and E. Teller. Equations of state of elements based on the generalized Fermi-Thomas theory, Phys. Rev. 75, 1561-1573 (1949)
  • [17] Einar Hille, Some aspects of the Thomas-Fermi equation, J. Analyse Math. 23 (1970), 147–170. MR 0279376, https://doi.org/10.1007/BF02795497
  • [18] A. Mambriani, Su un teorema relativo alle equazioni differenziali ordinarie del 2d ordine. Rend. Accad. Naz. del Lincei, CI. sci. fis., mat. e nat. (6) 9, 620-622 (1929)
  • [19] G. Scorza-Dragoni, Su un' equazione differenziale particolare, Rend. Accad. Naz. del Lincei, CI. sci. fis., mat. e nat. (6) 9, 623-625 (1929)
  • [20] James L. Reid, Solution to a nonlinear differential equation with application to Thomas-Fermi equations, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 53 (1972), 376–379 (1973) (English, with Italian summary). MR 0340691
  • [21] James L. Reid and Richard J. De Puy, Derivation of modified Thomas-Fermi and Emden equations, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 54 (1973), 529–532 (1974) (English, with Italian summary). MR 0355150
  • [22] M. Abramowitz and I. Stegun, Handbook of Mathematical functions, Dover, New York, 1965
  • [23] R. Courant and D. Hilbert, Methods of mathematical physics, Wiley, New York, 1953
  • [24] Samuel Karlin, Positive operators, J. Math. Mech. 8 (1959), 907–937. MR 0114138
  • [25] M. Krasnoselskii, Topological methods in nonlinear integral equations, Pergamon, New York, 1964

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 34B25, 81.34

Retrieve articles in all journals with MSC: 34B25, 81.34


Additional Information

DOI: https://doi.org/10.1090/qam/445056
Article copyright: © Copyright 1977 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website