Aperiodicity of the Hamiltonian flow in the Thomas-Fermi potential
type: Item
instance of: scholarly article
title: Aperiodicity of the Hamiltonian flow in the Thomas-Fermi potential
zbMATH Open document ID: 0788.34004
DOI: 10.4171/RMI/142
author: Charles Fefferman
author: L. Seco
published in: Revista Matemática Iberoamericana
publication date: 1994-05-26T00:00:00Z
full work available at URL: https://eudml.org/doc/39444
review text: Let \(y\) be the solution of the Thomas-Fermi differential equation \(y'' =x^{1/2} y^{3/2}\); \(y(0)=1\); \(y(\infty)=0\). Let \(\Omega^ 2_ c=\sup_{r>0}u(x)\); where \(u(x)= xy(x)\). Let \[ F(\Omega)=\int \left( {y \over x}-{\Omega^ 2 \over x^ 2} \right)_ +^{1/2}dx, \quad \Omega \in (0,\Omega_ c). \] The main result of the work is a proof of the inequality \(F''(\Omega) \leq c<0\;\forall \Omega \in (0,\Omega_ c)\). Computer aided analysis and a variety of conventional lemmas are supposed to prove this result in 143 pages. This result together with those in a further half-a-dozen papers to be published shortly will provide a proof of the asymptotic formula for the ground state energy of a nonrelativistic atom announced a few years ago by the same authors [Bull. Am. Math. Soc. 23, 525-530 (1990; Zbl 0722.35072)].
reviewed by: Chandra Shekhar Sharma
Mathematics Subject Classification ID: 34A25
Mathematics Subject Classification ID: 68T15
Mathematics Subject Classification ID: 81V45
Mathematics Subject Classification ID: 34A40
zbMATH DE Number: 482229
zbMATH Keywords: computer aided analysis
zbMATH Keywords: Thomas-Fermi differential equation
zbMATH Keywords: inequality
zbMATH Keywords: asymptotic formula
zbMATH Keywords: ground state energy of a nonrelativistic atom
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 482229