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On the leading energy correction for the statistical model of the atom: Interacting case. (English) Zbl 0920.35120
Summary: Introducing the Hellmann-Weizsäcker functional for large angular monenta and the orbitals of the Bohr atom for small angular momenta the authors obtain an upper bound on the quantum mechanical ground state energy of atoms that proves Scott’s conjecture (1952).

35Q40 PDEs in connection with quantum mechanics
81V45 Atomic physics
Full Text: DOI
[1] Hughes, W.: An atomic energy lower bound that proves Scott’s correction. Dissertation, Department of Mathematics, Princeton University 1986
[2] Scott, J.M.C.: The binding energy of the Thomas-Fermiatom. Phil. Mag.43, 859-867 (1952)
[3] Lieb, E.H., Simon, B.: The Thomas-Fermi theory of atoms, molecules and solids. Adv. Math.23, 22-116 (1977) · Zbl 0938.81568
[4] Lieb, E.H.: Thomas-Fermi and related theories of atoms and molecules. Rev. Mod. Phys.53, 603-641 (1981) · Zbl 1114.81336
[5] Thirring, W.: A lower bound with the best possible constant for Coulomb hamiltonians. Commun. Math. Phys.79, 1-7 (1981)
[6] Schwinger, J.: Thomas-Fermi model: The leading correction. Phys. Rev.A22, 1827-1832 (1980)
[7] Englert, B.-G., Schwinger, J.: Statistical atom: Handling the strongly bound electrons. Phys. Rev.A29, 2331-2338 (1984)
[8] Bander, M.: Corrections to the Thomas-Fermi model of the atom. Ann. Phys. (New York)144, 1-14 (1982)
[9] Siedentop, H.K.H., Weikard, R.: On some basic properties of density functionals for angular momentum channels, accepted for publication in Rep. Math. Phys. · Zbl 0644.46059
[10] Siedentop, H.K.H., Weikard, R.: On the behavior of the infimum of the Hellmann-Weizsäcker functional, Technical Report (1986) · Zbl 0925.35125
[11] Siedentop, H.K.H., Weikard, R.: On the leading energy correction for the statistical model of the atom: Non-interacting case. Abh. Braunschw. Wiss. Ges. (Germany)38, 145-158 (1986) · Zbl 0925.35125
[12] Lieb, E.H.: Variational principle for many-fermion systems. Phys. Rev. Lett.46, 457-459 (1981); Erratum. Phys. Rev. Lett.47, 69 (1981)
[13] Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Higher transcendal functions. I. New York: McGraw Hill 1953 · Zbl 0051.30303
[14] Englert, B.-G., Schwinger, J.: Atomic-binding-energy oscillations. Phys. Rev.A32, 47-63 (1985)
[15] Bochner, S.: Vorlesungen über Fouriersche Integrale. New York: Chelsea 1948 · JFM 58.0292.01
[16] Abramowitz, M., Stegun, I.: Handbook of mathematical functions. New York: Dover 1965 · Zbl 0171.38503
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