TY - JOUR

T1 - The Thomas-Fermi theory of atoms, molecules and solids

AU - Lieb, Elliott H.

AU - Simon, Barry

N1 - Funding Information:
* Work partially supported by National t A. Sloan Foundation Fellow; research grant MPS-75-11864.
Funding Information:
grant MPS 71-03375 A03. by the U.S. NSF. under

PY - 1977/1

Y1 - 1977/1

N2 - 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.

AB - 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.

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U2 - 10.1016/0001-8708(77)90108-6

DO - 10.1016/0001-8708(77)90108-6

M3 - Review article

AN - SCOPUS:33846040104

SN - 0001-8708

VL - 23

SP - 22

EP - 116

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

ER -