### Abstract

We place the Thomas-Fermi model of the quantum theory of atoms, molecules, and solids on a firm mathematical footing. Our results include: (1) A proof of existence and uniqueness of solutions of the nonlinear Thomas-Fermi equations as well as the fact that these solutions minimize the Thomas-Fermi energy functional, (2) a proof that in a suitable large nuclear charge limit, the quantum mechanical energy is asymptotic to the Thomas-Fermi energy, and (3) control of the thermodynamic limit of the Thomas-Fermi theory on a lattice.

Original language | English (US) |
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Pages (from-to) | 22-116 |

Number of pages | 95 |

Journal | Advances in Mathematics |

Volume | 23 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1977 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Lieb, E. H., & Simon, B. (1977). The Thomas-Fermi theory of atoms, molecules and solids.

*Advances in Mathematics*,*23*(1), 22-116. https://doi.org/10.1016/0001-8708(77)90108-6