Fefferman, Charles L.; Seco, Luis A. On the energy of a large atom. (English) Zbl 0722.35072 Bull. Am. Math. Soc., New Ser. 23, No. 2, 525-530 (1990). We announce a proof of an asymptotic formula for the groundstate energy of a large atom. The early work of Thomas-Fermi, Hartree-Fock, Dirac, and Scott predicted that for an atomic number Z, the energy is \(E(Z)\approx - c_ 0Z^{7/3}+c_ 1Z^ 2-c_ 2Z^{5/3}\) for known \(c_ 0,c_ 1\), and \(c_ 2\) [see E. H. Lieb, Rev. Mod. Phys 53, 603-641 (1981)]. J. Schwinger [Phys. Rev. A 24, 2353-2361 (1981)] observed an additional effect and set down the modified formula \(E(Z)\approx -c_ 0Z^{7/3}+c_ 1Z^ 2-(10/9)c_ 2Z^{5/3}\). Our proof shows that Schwinger’s formula is correct. Cited in 6 ReviewsCited in 31 Documents MSC: 35Q40 PDEs in connection with quantum mechanics 81V45 Atomic physics 81Q15 Perturbation theories for operators and differential equations in quantum theory Keywords:asymptotic formula; groundstate energy; large atom × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Webster Hughes, An atomic energy lower bound that agrees with Scott’s corrections, Adv. Math. 79 (1990), no. 2, 213 – 270. · Zbl 0715.46046 · doi:10.1016/0001-8708(90)90063-S [2] C. L. Fefferman and L. A. Seco, An upper bound for the number of electrons in a large ion, Proc. Nat. Acad. Sci. U.S.A. 86 (1989), no. 10, 3464 – 3465. · doi:10.1073/pnas.86.10.3464 [3] Charles L. Fefferman and Luis A. Seco, Asymptotic neutrality of large ions, Comm. Math. Phys. 128 (1990), no. 1, 109 – 130. · Zbl 0695.60098 [4] Elliott H. Lieb, A lower bound for Coulomb energies, Phys. Lett. A 70 (1979), no. 5-6, 444 – 446. · doi:10.1016/0375-9601(79)90358-X [5] Elliott H. Lieb, Thomas-Fermi and related theories of atoms and molecules, Rev. Modern Phys. 53 (1981), no. 4, 603 – 641. , https://doi.org/10.1103/RevModPhys.53.603 Elliott H. Lieb, Erratum: ”Thomas-Fermi and related theories of atoms and molecules”, Rev. Modern Phys. 54 (1982), no. 1, 311. · Zbl 1049.81679 · doi:10.1103/RevModPhys.54.311 [6] Elliott H. Lieb and Barry Simon, The Thomas-Fermi theory of atoms, molecules and solids, Advances in Math. 23 (1977), no. 1, 22 – 116. · Zbl 0938.81568 · doi:10.1016/0001-8708(77)90108-6 [7] Julian Schwinger, Thomas-Fermi model: the second correction, Phys. Rev. A (3) 24 (1981), no. 5, 2353 – 2361. · doi:10.1103/PhysRevA.24.2353 [8] L. A. Seco, I. M. Sigal, and J. P. Solovej, Bound on the ionization energy of large atoms, Comm. Math. Phys. 131 (1990), no. 2, 307 – 315. · Zbl 0714.35059 [9] Heinz Siedentop and Rudi Weikard, On the leading energy correction for the statistical model of the atom: interacting case, Comm. Math. Phys. 112 (1987), no. 3, 471 – 490. · Zbl 0920.35120 [10] Heinz Siedentop and Rudi Weikard, On the leading correction of the Thomas-Fermi model: lower bound, Invent. Math. 97 (1989), no. 1, 159 – 193. With an appendix by A. M. Klaus Müller. · Zbl 0689.34011 · doi:10.1007/BF01850659 [11] H. Siedentop and R. Weikard, A lower bound of Scott type by a new microlocalization technique (to appear). · Zbl 0802.35128 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.