ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Of concern is a rigorous Thomas–Fermi theory of electron densities for spin-polarized quantum-mechanical systems. The number N↑, N↓ of spin-up and spin-down electrons are specified in advance, and one seeks to minimize the energy functional E(ρ↑,ρ↓) =c1∫R3(ρ↑(x)5/3 +ρ↓(x)5/3)dx +c2∫R3∫R3[ρ(x)ρ(y)/||x −y||]dx dy +∫R3V(x)ρ(x)dx, where c1, c2 are given positive constants, ρ↑ and ρ↓ are non-negative functions, ρ=ρ↑ +ρ↓ is the total electron density, ∫R3ρ↑(x)dx =N↑, ∫R3ρ↓(x)dx =N↓, and V is a given potential. These results are analogous to the classical rigorous (spin-unpolarized) Thomas–Fermi theory developed by Lieb and Simon [Phys. Rev. Lett. 33, 681 (1973)] and by Bénilan and Brezis ("The Thomas–Fermi problem,'' in preparation).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.528011
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