Differential and Integral Equations

Thomas-Fermi theory with magnetic fields and the Fermi-Amaldi correction

Gisèle Ruiz Goldstein, Jerome A. Goldstein, and Wenyao Jia

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Of concern is a quantum mechanical system having $N_{1}$ (resp. $N_{2}$) spin up (resp. spin down) electrons, in the presence of a potential $V$ and a magnetic field $B.$ When the Fermi-Amaldi correction is incorporated into the Thomas-Fermi energy functional, convexity is lost and the computation of the ground state spin up and down electron densities becomes nontrivial. We discuss the existence of these densities and various approximation procedures for them, via variational calculus, differential equations, and numerical procedures.

Article information

Differential Integral Equations, Volume 8, Number 6 (1995), 1305-1316.

First available in Project Euclid: 15 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 81V45: Atomic physics
Secondary: 49S05: Variational principles of physics (should also be assigned at least one other classification number in section 49) 81V55: Molecular physics [See also 92E10]


Goldstein, Gisèle Ruiz; Goldstein, Jerome A.; Jia, Wenyao. Thomas-Fermi theory with magnetic fields and the Fermi-Amaldi correction. Differential Integral Equations 8 (1995), no. 6, 1305--1316. https://projecteuclid.org/euclid.die/1368638167

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