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Thomas-Fermi theory for matter in a magnetic field as a limit of quantum mechanics. (English) Zbl 0729.60114

Summary: 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 electrons 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 \(a\to \infty\). A similar result holds also for the electronic density. This generalizes corresponding theorems for zero magnetic field due to Lieb, Simon, and Baumgartner.

MSC:

60K40 Other physical applications of random processes
81S25 Quantum stochastic calculus
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
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