Semi-classical limit theorems for Hartree-Fock theory. (English) Zbl 0539.47028
In the paper the author used the technique of Sobolev inequalities and strongly continuous semi-groups to relate the Hartree-Fock exchange energy to the Dirac exchange energy. It is shown that the exchange energy for the Hartree-Fock ground state of the large number of electrons with Coulomb repulsion moving under the influence of static nuclei converges in a suitable limit to the formula obtained by Dirac for exchange energy as an integral of the one body density.
At first the author considers the simple case of a large number of fermions with no mutual interaction moving under the influence of a nonlocal potential. Then he extends his method to the general case.
At first the author considers the simple case of a large number of fermions with no mutual interaction moving under the influence of a nonlocal potential. Then he extends his method to the general case.
Reviewer: V.Sobolev
MSC:
| 47L90 | Applications of operator algebras to the sciences |
| 46N99 | Miscellaneous applications of functional analysis |
| 81V80 | Quantum optics |
Keywords:
semi-classical limit; Coulomb system; Coulomb energy; Sobolev inequalities; strongly continuous semi-groups; Hartree-Fock exchange energy; Dirac exchange energyReferences:
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