## Differential and Integral Equations

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

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

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

#### 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

**Subjects**

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]

#### 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