ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Of concern is a rigorous Thomas–Fermi theory of ground state electron densities for quantum mechanical systems in an external magnetic field. The energy functional takes the form E(ρ1,ρ2)=∑2i=1ci ∫R3ρi (x)5/3 dx + (1)/(2) ∫R3∫R3[ρ(x)ρ(y)/||x−y||]dx dy +∫R3V(x)ρ(x)dx +∫R3(B(x)(ρ1(x)−ρ2(x))dx; here ci is a positive constant, ρ1 [resp. ρ2] is the density of spin-up [resp. spin-down] electrons, ρ=ρ1+ρ2 is the total electron density, V is a given potential (typically a Coulomb potential describing electron–nuclear attraction), and B describes the effect of the external magnetic field. Let Ni=∫R3ρi(x)dx be the number of spin-up and spin-down electrons for i=1,2, and let N=N1+N2 be the total number of electrons. Specifying N and minimizing E(ρ1,ρ2) generally leads to a spin polarized system. For example, if B≤0 and B(large-closed-square)0, then ρ1≥ρ2 and N1〉N2. This and a number of related results are proved.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.529084
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