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Nonlinear Semigroups, Partial Differential Equations and Attractors pp 68–82Cite as

Recent rigorous results in Thomas-Fermi theory

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References

  1. Bénilan, Ph. and H. Brezis, The Thomas-Fermi problem, in preparation.

    Google Scholar 

  2. Bénilan, Ph., H. Brezis, and M. G. Crandall, A semilinear elliptic equation in L1(IRN), Ann. Scuola Norm. Sup. Pisa 2 (1975), 523–555.

    MATH  Google Scholar 

  3. Bethe, H. and R. W. Jackiw, Intermediate Quantum Mechanics, Benjamin, New York, 1968.

    Google Scholar 

  4. Brezis, H., Nonlinear problems related to the Thomas-Fermi equation, in Contemporary Developments in Continuum Mechanics and Partial Differential Equations (ed. by G. M. de la Penha and L. A. Medeiros), North-Holland, Amsterdam (1978), 81–89.

    Google Scholar 

  5. Brezis, H., Some variational problems of Thomas-Fermi type, in Variational Inequalities and Complementary Problems: Theory and Applications (ed. by R. W. Cottle, F. Giannessi and J. L. Lions), Wiley, New York (1980), 53–73.

    Google Scholar 

  6. Fermi, E., Un methodo statistico per la determinazione di alcune prioretà dell' atome, Rend. Acad. Naz. Lincei (1927), 602–607.

    Google Scholar 

  7. Fermi, E. and E. Amaldi, Le orbite ∞s degli elementi, Mem. Accad. d'Italia 6 (1934), 119–149.

    MATH  Google Scholar 

  8. Gadiyak, G. V. and Yu. E. Lozovik, Many-electron atoms in high magnetic fields, J. Phys. B, Molec. Phys. 13 (1980), 1531–1535.

    Article  Google Scholar 

  9. 9.Gallouët, Th. and J.-M. Morel, On some properties of the solution of the Thomas-Fermi problem, in Nonlinear Analysis, Theory, Methods and Applications, 7 (1983), 971–979.

    Article  MathSciNet  MATH  Google Scholar 

  10. Goldstein, J. A. and G. R. Rieder, Some extensions of Thomas-Fermi theory, in Proceedings of the Conference on Differential Equations in Banach Spaces (ed. by A. Favini and E. Obrecht), Springer Lecture Notes in Mathematics 1223, Berlin (1986), 110–121.

    Google Scholar 

  11. Goldstein, J. A. and G. R. Rieder, The Coulomb potential in higher dimensions, in Proceedings of the International Conference on Differential Equations and Mathematical Physics (ed. by I. W. Knowles and Y. Saito), Springer Lecture Notes in Mathematics 1285, New York (1987), 143–149.

    Google Scholar 

  12. Goldstein, J. A. and G. R. Rieder, A class of ordinary differential equations connected with Thomas-Fermi theory, Matem. Aplic. Comp. 6 (1987), 57–68.

    MathSciNet  MATH  Google Scholar 

  13. Goldstein, J. A. and G. R. Rieder, A rigorous modified Thomas-Fermi theory for atomic systems, J. Math. Phys. 28 (1987), 1198–1202.

    Article  MathSciNet  MATH  Google Scholar 

  14. Goldstein, J. A. and G. R. Rieder, Spin polarized Thomas-Fermi theory, J. Math. Phys. 29 (1988), 709–716.

    Article  MathSciNet  MATH  Google Scholar 

  15. Landau, L. D. and E. M. Lifschitz, Quantum Mechanics. Non-Relativistic Theory (2nd ed.), Pergamon, Oxford and New York, 1965.

    Google Scholar 

  16. Lieb, E. H., Thomas-Fermi theory and related theories of atoms and molecules, Rev. Mod. Phys. 53 (1981), 603–641.

    Article  MathSciNet  MATH  Google Scholar 

  17. Lieb, E. H. and B. Simon, Thomas-Fermi theory revisited, Phys. Rev. Lett. 33 (1973), 681–683.

    Article  Google Scholar 

  18. Lieb, E. H. and B. Simon, The Thomas-Fermi theory of atoms, molecules, and solids, Adv. Math. 23 (1977), 22–116.

    Article  MathSciNet  MATH  Google Scholar 

  19. Oliver, G. L. and J. P. Perdew, Spin-density gradient expansion for the kinetic energy, Phys. Rev. A 20 (1979), 397–403.

    Article  Google Scholar 

  20. Parr, R. G. and S. K. Ghosh, Thomas-Fermi theory for atomic systems, Proc. Nat. Acad. Sci. USA 83 (1983), 3577–3579.

    Article  Google Scholar 

  21. Pathak, R., Some Investigations on Atoms and Molecules within the Density Functional Formalism, Ph.D. Thesis, Univ. of Poona, Pune, India, 1982.

    Google Scholar 

  22. Perdew, J. P. and Yue Wang, Electron density functionals from the gradient expansion of the density matrix: The trouble with long range iterations, in Mathematics Applied to Science (ed. by J. A. Goldstein, S. I. Rosencrans, and G. A. Sod), Academic Press, Boston (1988), 187–210.

    Google Scholar 

  23. Pratt, L. R., G. G. Hoffman, and R. A. Harris, The statistical theory of electron densities, J. Chem. Phys. 88 (1988), 1818–1823.

    Article  Google Scholar 

  24. Rieder, G. R., Mathematical contributions to Thomas-Fermi theory, Houston J. Math., in press.

    Google Scholar 

  25. Thomas, L. H., The calculation of atomic fields, Proc. Cambridge Phil. Soc. 23 (1927), 542–548.

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Quantum Theory Group, Tulane University, 70118, New Orleans, LA

    Jerome A. Goldstein

  2. Department of Mathematics, Louisiana State University, 70803, Baton Rouge, LA

    Gisèle Ruiz Rieder

Authors
  1. Jerome A. Goldstein
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  2. Gisèle Ruiz Rieder
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Editor information

Tepper L. Gill Woodford William Zachary

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© 1989 Springer-Verlag

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Goldstein, J.A., Rieder, G.R. (1989). Recent rigorous results in Thomas-Fermi theory. In: Gill, T.L., Zachary, W.W. (eds) Nonlinear Semigroups, Partial Differential Equations and Attractors. Lecture Notes in Mathematics, vol 1394. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086753

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  • DOI: https://doi.org/10.1007/BFb0086753

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  • Print ISBN: 978-3-540-51594-4

  • Online ISBN: 978-3-540-46679-6

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