## Differential and Integral Equations

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

#### Abstract

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

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

Dates
First available in Project Euclid: 15 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1368638167

Mathematical Reviews number (MathSciNet)
MR1329842

Zentralblatt MATH identifier
0863.49032

#### Citation

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