The mathematics of large atoms
Journées équations aux dérivées partielles (1995), article no. 11, 12 p.
@article{JEDP_1995____A11_0,
     author = {Fefferman, Charles L. and Seco, Luis A.},
     title = {The mathematics of large atoms},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {11},
     publisher = {Ecole polytechnique},
     year = {1995},
     mrnumber = {1360480},
     language = {en},
     url = {http://archive.numdam.org/item/JEDP_1995____A11_0/}
}
TY  - JOUR
AU  - Fefferman, Charles L.
AU  - Seco, Luis A.
TI  - The mathematics of large atoms
JO  - Journées équations aux dérivées partielles
PY  - 1995
DA  - 1995///
PB  - Ecole polytechnique
UR  - http://archive.numdam.org/item/JEDP_1995____A11_0/
UR  - https://www.ams.org/mathscinet-getitem?mr=1360480
LA  - en
ID  - JEDP_1995____A11_0
ER  - 
%0 Journal Article
%A Fefferman, Charles L.
%A Seco, Luis A.
%T The mathematics of large atoms
%J Journées équations aux dérivées partielles
%D 1995
%I Ecole polytechnique
%G en
%F JEDP_1995____A11_0
Fefferman, Charles L.; Seco, Luis A. The mathematics of large atoms. Journées équations aux dérivées partielles (1995), article  no. 11, 12 p. http://archive.numdam.org/item/JEDP_1995____A11_0/

[Ba] Bach, V. «Accuracy of Mean Field Approximations for Atoms and Molecules» Comm. Math. Phys. 155 no. 2, 295-310 (1993). | MR | Zbl

[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. | MR | Zbl

[CFS2] Córdoba, A., Fefferman, C., Seco, L., «Weyl Sums and Atomic Energy Oscillations» Revista Matemática Iberoamericana, Vol 11, no. 1. (1995) ; pp 167-228. | MR | Zbl

[CFS2] Córdoba, A., Fefferman, C., Seco, L., «A Number-Theoretic Estimate for the Thomas-Fermi Density» To appear. | Zbl

[En] Englert, B. G. «Semiclassical Theory of the Atom» Springer Verlag Lecture Notes in Physics, vol 301.

[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. | MR | Zbl

[FS2] Fefferman, C. and Seco, L. «Eigenvalues and Eigenfunctions of Ordinary Differential Operators» Adv. Math. Vol 95 no. 2, 145-305 (1992). | MR | Zbl

[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. | MR | Zbl

[FS4] Fefferman, C. and Seco, L. «The Density in a One-Dimensional Potential» Advances in Math., Vol 107 no. 2, Sep 1994, 187-364. | MR | Zbl

[FS5] Fefferman, C. and Seco, L. «The Eigenvalue Sum for a Three-Dimensional Radial Potential» To appear in Adv. Math. | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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). | MR | Zbl

[F1] Fefferman, C. «Atoms and Analytic Number Theory» A.M.S. Centennial Publication Vol. II (1992), 27-36. | MR | Zbl

[Fe] Fermi, E. (1927) «Un Metodo Statistico per la Determinazione di alcune Priorieta dell'Atome» Rend. Accad. Naz. Lincei 6, 602-607.

[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. | MR | Zbl

[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. | MR | Zbl

[HL] Heilmann and Lieb «Preprint.».

[Hu] Hughes, W. «An Atomic Energy Lower Bound that Agrees with Scott's Correction.» Advances in Mathematics, 79, 213-270, 1990. | MR | Zbl

[ILS] A. Iantchenko, E. Lieb and H. Siedentop «Proof of the Strong Scott Conjecture for Atomic and Molecular Cores» Preprint.

[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). | MR | Zbl

[LS] Lieb, E. and Simon, B. (1977) «Thomas-Fermi Theory of Atoms, Molecules and Solids» Adv. Math. 23, pp 22-116. | MR | Zbl

[Li] Lieb, E. (1981) «Thomas-Fermi and Related Theories of Atoms and Molecules» Reviews of Modern Physics Vol 53 no. 4, 603-641. | MR | Zbl

[Sch] Schwinger, J. (1981) «Thomas-Fermi Model: The Second Correction» Physical Review A24, 5, 2353-2361. | MR

[Sc] Scott, J. M. C. (1952) «The Binding Energy of the Thomas-Fermi Atom» Phil. Mag. 43 859-867.

[SW1] Siedentop, H., Weikard, R. «On the Leading Energy Correction for the Statistical Model of the Atom: Interacting Case» Communications in Mathematical Physics 112 471-490 (1987). | MR | Zbl

[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). | MR | Zbl

[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). | Numdam | Zbl

[Th] Thomas, L. H. (1927) «The Calculation of Atomic Fields» Proc. Cambridge Philos. Soc. 23 542-548. | JFM