@article{JEDP_1995____A11_0, author = {Fefferman, Charles Louis and Seco, Luis A.}, title = {The mathematics of large atoms}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, year = {1995}, pages = {1-12}, mrnumber = {1360480}, language = {en}, url = {http://dml.mathdoc.fr/item/JEDP_1995____A11_0} }
Fefferman, Charles L.; Seco, Luis A. The mathematics of large atoms. Journées équations aux dérivées partielles, (1995), pp. 1-12. http://gdmltest.u-ga.fr/item/JEDP_1995____A11_0/
[Ba] «Accuracy of Mean Field Approximations for Atoms and Molecules» Comm. Math. Phys. 155 no. 2, 295-310 (1993). | MR 94f:81183 | Zbl 0802.47061
[CFS1] «A Trigonometric Sum relevant to the Non-relativistic Theory of Atoms» Proc. Nat. Acad. Sci. USA, Vol. 91, 5776-5778, June 1994. | MR 95i:81281 | Zbl 0827.11079
, , ,[CFS2] «Weyl Sums and Atomic Energy Oscillations» Revista Matemática Iberoamericana, Vol 11, no. 1. (1995) ; pp 167-228. | MR 95k:81029 | Zbl 0836.11028
, , ,[CFS2] «A Number-Theoretic Estimate for the Thomas-Fermi Density» To appear. | Zbl 0857.35105
, , ,[En] «Semiclassical Theory of the Atom» Springer Verlag Lecture Notes in Physics, vol 301.
[FS1] «The Ground-State Energy of a Large Atom» Bull. A.M.S., Vol 23 no. 2, 525-530, 1990. | MR 92a:81230 | Zbl 0722.35072
and[FS2] «Eigenvalues and Eigenfunctions of Ordinary Differential Operators» Adv. Math. Vol 95 no. 2, 145-305 (1992). | MR 93j:34121 | Zbl 0797.34083
and[FS3] «The Eigenvalue Sum for a One-Dimensional Potential» Advances in Math, Vol. 108 no. 2, Oct 1994 ; 263-335. | MR 95j:81049 | Zbl 0826.34070
and[FS4] «The Density in a One-Dimensional Potential» Advances in Math., Vol 107 no. 2, Sep 1994, 187-364. | MR 96a:81147 | Zbl 0811.34063
and[FS5] «The Eigenvalue Sum for a Three-Dimensional Radial Potential» To appear in Adv. Math. | Zbl 0845.34086
and[FS6] «The Density in a Three-Dimensional Radial Potential» Advances in Math., Vol 111 no. 1, March 1995, 88-161. | MR 95j:81050 | Zbl 0826.34071
and[FS7] «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 95e:81262 | Zbl 0820.35113
and[FS8] «Aperiodicity of the Hamiltonian Flow in the Thomas-Fermi Potential» Revista Matemática Iberoamericana, Vol 9 no. 3, 409-551 (1993). | MR 95g:35170 | Zbl 0788.34004
and[F1] «Atoms and Analytic Number Theory» A.M.S. Centennial Publication Vol. II (1992), 27-36. | MR 93g:81017 | Zbl 1071.81515
[Fe] «Un Metodo Statistico per la Determinazione di alcune Priorieta dell'Atome» Rend. Accad. Naz. Lincei 6, 602-607.
(1927)[GS] «A Correlation Estimate with Applications to Quantum Systems with Coulomb Interactions» Reviews in Math. Phys. Vol 6, No 5a (1994), 977-997. | MR 96b:81138 | Zbl 0843.47041
and[GK] «Van der Corput's Method of Exponential Sums» Cambridge University Press. London Math. Soc. Lecture Notes Series, 126. | MR 92k:11082 | Zbl 0713.11001
and[HL]
and «Preprint.».[Hu] «An Atomic Energy Lower Bound that Agrees with Scott's Correction.» Advances in Mathematics, 79, 213-270, 1990. | MR 91c:81180 | Zbl 0715.46046
[ILS] «Proof of the Strong Scott Conjecture for Atomic and Molecular Cores» Preprint.
and[IS] «Asymptotics of the Ground State Energies of Large Coulomb Systems» Annals of Math. Vol. 138 no. 2, 243-335 (1993). | MR 95a:81302 | Zbl 0789.35135
and[LS] «Thomas-Fermi Theory of Atoms, Molecules and Solids» Adv. Math. 23, pp 22-116. | MR 55 #1964 | Zbl 0938.81568
and , B. (1977)[Li] «Thomas-Fermi and Related Theories of Atoms and Molecules» Reviews of Modern Physics Vol 53 no. 4, 603-641. | MR 83a:81080a | Zbl 1049.81679
(1981)[Sch] «Thomas-Fermi Model: The Second Correction» Physical Review A24, 5, 2353-2361. | MR 83a:81081
(1981)[Sc] «The Binding Energy of the Thomas-Fermi Atom» Phil. Mag. 43 859-867.
(1952)[SW1] «On the Leading Energy Correction for the Statistical Model of the Atom: Interacting Case» Communications in Mathematical Physics 112 471-490 (1987). | MR 89a:81022 | Zbl 0920.35120
,[SW2] «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 90k:81285 | Zbl 0689.34011
,[SW3] «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 0762.47022
, (1990)[Th] «The Calculation of Atomic Fields» Proc. Cambridge Philos. Soc. 23 542-548. | JFM 53.0868.04
(1927)