Heavy molecules in the strong magnetic field
type: Item
instance of: scholarly article
title: Heavy molecules in the strong magnetic field
zbMATH Open document ID: 0908.35106
published in: Russian Journal of Mathematical Physics
publication date: 1999-01-12T00:00:00Z
review text: The author announces results on the asymptotics of the ground state energy of atoms and molecules with large atomic numbers \(Z_1,\dots,Z_M\) in the presence of strong homogeneous magnetic fields. His main claim is that the sum of the Thomas-Fermi energy plus the Scott correction, \( \kappa_{\text{Scott}}(Z_1^2+\dots+Z_M^2)\), is the leading contribution as long as the \(Z_j\) are bounded from above and below by a constant times the particle number \(N\), as long as \(B=O(N^3)\), and as long as the nuclei are not too close together. This estimates leads in a natural way to an estimate on the the difference of the quantum particle density and the Thomas-Fermi density which in turn implies an asymptotic bound on the ionization energy and the excess charge. The author also claims a bound on the minimal number of electrons that are necessary to have binding of molecules.
reviewed by: Heinz Siedentop
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 81V55
zbMATH DE Number: 1206194
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: Scott correction
author: Victor Ivrii
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1206194