The Thomas-Fermi theory of atoms, molecules and solids

Elliott HLieb^12∗BarrySimon^12†

¹

Department of Mathematics, Princeton University, Princeton, New Jersey 08540 USA

²

Department of Physics, Princeton University, Princeton, New Jersey 08540 USA

Available online 2 July 2004.

 

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.

 

 https://sci-hub.se/https://doi.org/10.1016/0001-8708(77)90108-6