Thomas-Fermi theory for matter in a magnetic field as a limit of quantum mechanics

✍ Scribed by Jakob Yngvason

• Publisher: Springer
• Year: 1991
• Tongue: English
• Weight: 479 KB
• Volume: 22
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00405174

✦ Synopsis

The Thomas-Fermi theory for electrons and fixed nuclei in a homogeneous magnetic field is shown to be a limit of quantum mechanics in the following sense: If the nuclear charges and the number of eletrons are multiplied by a, and the magnetic field by a 4/3, then the ground-state energy, divided by a 7;3, converges to the TF energy when a --, 0o. A similar result holds also for the electronic density. This generalizes corresponding theorems for zero magnetic field due to Lieb, Simon, and Baumgartner.

AMS subject classifications (1991). 8lSxx, 82C05.