The Thomas-Fermi theory of atoms, molecules and solids

Elliott H. Lieb, Barry Simon

Research output: Contribution to journalReview article

392 Scopus citations

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 languageEnglish (US)
Pages (from-to)22-116
Number of pages95
JournalAdvances in Mathematics
Volume23
Issue number1
DOIs
StatePublished - Jan 1977

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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