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The mathematics of large atoms

Charles L. Fefferman; Luis A. Seco

Journées équations aux dérivées partielles (1995)

  • Volume: 1995, page 1-12
  • ISSN: 0752-0360

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Fefferman, Charles L., and Seco, Luis A.. "The mathematics of large atoms." Journées équations aux dérivées partielles 1995 (1995): 1-12. <http://eudml.org/doc/93296>.

@article{Fefferman1995,
author = {Fefferman, Charles L., Seco, Luis A.},
journal = {Journées équations aux dérivées partielles},
keywords = {Thomas-Fermi potential; Thomas-Fermi theory; large- asymptotics},
language = {eng},
pages = {1-12},
publisher = {Ecole polytechnique},
title = {The mathematics of large atoms},
url = {http://eudml.org/doc/93296},
volume = {1995},
year = {1995},
}

TY - JOUR
AU - Fefferman, Charles L.
AU - Seco, Luis A.
TI - The mathematics of large atoms
JO - Journées équations aux dérivées partielles
PY - 1995
PB - Ecole polytechnique
VL - 1995
SP - 1
EP - 12
LA - eng
KW - Thomas-Fermi potential; Thomas-Fermi theory; large- asymptotics
UR - http://eudml.org/doc/93296
ER -

References

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  2. [CFS1] Córdoba, A., Fefferman, C., Seco, L., «A Trigonometric Sum relevant to the Non-relativistic Theory of Atoms» Proc. Nat. Acad. Sci. USA, Vol. 91, 5776-5778, June 1994. Zbl0827.11079MR95i:81281
  3. [CFS2] Córdoba, A., Fefferman, C., Seco, L., «Weyl Sums and Atomic Energy Oscillations» Revista Matemática Iberoamericana, Vol 11, no. 1. (1995) ; pp 167-228. Zbl0836.11028MR95k:81029
  4. [CFS2] Córdoba, A., Fefferman, C., Seco, L., «A Number-Theoretic Estimate for the Thomas-Fermi Density» To appear. Zbl0857.35105
  5. [En] Englert, B. G.«Semiclassical Theory of the Atom» Springer Verlag Lecture Notes in Physics, vol 301. 
  6. [FS1] Fefferman, C. and Seco, L.«The Ground-State Energy of a Large Atom» Bull. A.M.S., Vol 23 no. 2, 525-530, 1990. Zbl0722.35072MR92a:81230
  7. [FS2] Fefferman, C. and Seco, L.«Eigenvalues and Eigenfunctions of Ordinary Differential Operators» Adv. Math. Vol 95 no. 2, 145-305 (1992). Zbl0797.34083MR93j:34121
  8. [FS3] Fefferman, C. and Seco, L.«The Eigenvalue Sum for a One-Dimensional Potential» Advances in Math, Vol. 108 no. 2, Oct 1994 ; 263-335. Zbl0826.34070MR95j:81049
  9. [FS4] Fefferman, C. and Seco, L.«The Density in a One-Dimensional Potential» Advances in Math., Vol 107 no. 2, Sep 1994, 187-364. Zbl0811.34063MR96a:81147
  10. [FS5] Fefferman, C. and Seco, L.«The Eigenvalue Sum for a Three-Dimensional Radial Potential» To appear in Adv. Math. Zbl0845.34086
  11. [FS6] Fefferman, C. and Seco, L.«The Density in a Three-Dimensional Radial Potential» Advances in Math., Vol 111 no. 1, March 1995, 88-161. Zbl0826.34071MR95j:81050
  12. [FS7] Fefferman, C. and Seco, L.«On the Dirac and Schwinger Corrections to the Ground-State Energy of an Atom» Advances in Math., Vol 107 no. 1, Aug 1994, 1-185. Zbl0820.35113MR95e:81262
  13. [FS8] Fefferman, C. and Seco, L.«Aperiodicity of the Hamiltonian Flow in the Thomas-Fermi Potential» Revista Matemática Iberoamericana, Vol 9 no. 3, 409-551 (1993). Zbl0788.34004MR95g:35170
  14. [F1] Fefferman, C.«Atoms and Analytic Number Theory» A.M.S. Centennial Publication Vol. II (1992), 27-36. Zbl1071.81515MR93g:81017
  15. [Fe] Fermi, E. (1927) «Un Metodo Statistico per la Determinazione di alcune Priorieta dell'Atome» Rend. Accad. Naz. Lincei 6, 602-607. 
  16. [GS] Graf, G. M. and Solovej, J. P.«A Correlation Estimate with Applications to Quantum Systems with Coulomb Interactions» Reviews in Math. Phys. Vol 6, No 5a (1994), 977-997. Zbl0843.47041MR96b:81138
  17. [GK] S. W. Graham and G. Kolesnik«Van der Corput's Method of Exponential Sums» Cambridge University Press. London Math. Soc. Lecture Notes Series, 126. Zbl0713.11001MR92k:11082
  18. [HL] Heilmann and Lieb «Preprint.». 
  19. [Hu] Hughes, W.«An Atomic Energy Lower Bound that Agrees with Scott's Correction.» Advances in Mathematics, 79, 213-270, 1990. Zbl0715.46046MR91c:81180
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  21. [IS] Ivrii, V. and Sigal, I. M.«Asymptotics of the Ground State Energies of Large Coulomb Systems» Annals of Math. Vol. 138 no. 2, 243-335 (1993). Zbl0789.35135MR95a:81302
  22. [LS] Lieb, E. and Simon, B. (1977) «Thomas-Fermi Theory of Atoms, Molecules and Solids» Adv. Math. 23, pp 22-116. Zbl0938.81568MR55 #1964
  23. [Li] Lieb, E. (1981) «Thomas-Fermi and Related Theories of Atoms and Molecules» Reviews of Modern Physics Vol 53 no. 4, 603-641. Zbl1049.81679MR83a:81080a
  24. [Sch] Schwinger, J. (1981) «Thomas-Fermi Model: The Second Correction» Physical Review A24, 5, 2353-2361. MR83a:81081
  25. [Sc] Scott, J. M. C. (1952) «The Binding Energy of the Thomas-Fermi Atom» Phil. Mag. 43 859-867. 
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  27. [SW2] Siedentop, H., Weikard, R.«On the Leading Correction of the Thomas-Fermi Model: Lower Bound» and an appendix by A.M.K. Müller. Inv. Math., Vol., 97, pp 159-193 (1989). Zbl0689.34011MR90k:81285
  28. [SW3] Siedentop, H., Weikard, R. (1990) «A New Phase Space Localization Technique with Applications to the Sum of Negative Eigenvalues of Schrödinger Operators.» Ann. Scient. Ecole Normale Superieure 24, 215-225, (1991). Zbl0762.47022
  29. [Th] Thomas, L. H. (1927) «The Calculation of Atomic Fields» Proc. Cambridge Philos. Soc. 23 542-548. Zbl53.0868.04JFM53.0868.04

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