## Abstract

In this article, I’d like to motivate some work that Luis Seco and I have done on the ground-state energy of an atom of atomic number Z ≫ 1. If one ignores relativistic effects, then the mathematical problem is as follows. Fix a nucleus of charge +
We regard the electrons as quantized, so that the state of the system is given by a wave function
For simplicity, we neglect spin here. (If we had taken spin into account, then ψ would take values in the ψ-fold tensor power of ℂ

*Z*at the origin. If*N*electrons are located at*x*_{1},*x*_{2},…,*x*_{N}∈ ℝ^{3}, then their potential energy is given by$$
V_{Coulomb}^{NZ} (x_{1,...,} x_N ) = - \sum\limits_{k = 1}^N {\frac{z}
{{|x_k |}}} + \sum\limits_{1 \leqslant j < k \leqslant N} {\frac{1}
{{|x_j - x_k |}}.}
$$

(1)

$$ \psi \left( {{x_1}, \ldots, {x_N}} \right) \in {L^2}\left( {{\mathbb{R}^{{3N}}}} \right) $$

^{2}. This changes no ideas, but introduces factors of 2 into some key formulas).## Keywords

Atomic Number Periodic Table Lower Eigenvalue Electron Repulsion Small Irregularity
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## References

- [FS1]C. Fefferman and L. Seco,
*The ground-state energy of a large atom*, Bull. A.M.S.**23**(2) (1990), 525–530.MathSciNetMATHCrossRefGoogle Scholar - [FS2]C. Fefferman and L. Seco,
*Eigenvalues and eigenfunctions of ordinary differential operators*, Adv. Math.**95**(1992), 145–305.MathSciNetMATHCrossRefGoogle Scholar - [FS3]C. Fefferman and L. Seco,
*On the Dirac and Schwinger corrections to the ground-state energy of an atom*, Adv. Math.**107**(1994), 1–185.MathSciNetMATHCrossRefGoogle Scholar - [FS4]C. Fefferman and L. Seco,
*The density in a one-dimensional potential*, Adv. Math.**107**(2) (1994), 187–364.MathSciNetMATHCrossRefGoogle Scholar - [FS5]C. Fefferman and L. Seco,
*The eigenvalue sum for a one-dimensional potential*, Adv. Math.**108**(2) (1994), 263–335.MathSciNetMATHCrossRefGoogle Scholar - [FS6]C. Fefferman and L. Seco,
*Aperiodicity of the Hamiltonian flow in the Thomas-Fermi potential*, Rev. Math. Iberoam.**9**(3) (1993), 409–551.MathSciNetMATHGoogle Scholar - [FS7]C. Fefferman and L. Seco,
*The density in a three-dimensional radial potential*, Adv. Math.**111**(1) (1995), 88–161.MathSciNetMATHCrossRefGoogle Scholar - [FS8]C. Fefferman and L. Seco,
*The eigenvalue sum for three-dimensional radial potential*, Adv. Math.**119**(1) (1996), 26–116.MathSciNetMATHCrossRefGoogle Scholar - [IS]V. Ivrii and I. M. Sigal,
*Asymptotics of the gound state energies of large Coulomb systems*, Annals of Math.**138**(1993), 243–335.MathSciNetMATHCrossRefGoogle Scholar - [L]E. Lieb,
*Thomas-Fermi and related theories of atoms and molecules*, I, Rev. Mod. Phys.**53**(4) (1981), 603–641.MathSciNetMATHCrossRefGoogle Scholar

## Copyright information

© Birkhäuser Boston 1999