Analysis of the Thomas-Fermi-von Weizsäcker equation for an infinite atom without electron repulsion

Elliott H. Lieb

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Abstract

The equation {Mathematical expression} in three dimensions is investigated. Uniqueness and other properties of the positive solution are proved for 3/2<p<2. There are two physical interpretations of this equation for p=5/3: (i) As the TFW equation for an infinite atom without electron repulsion; (ii) The positive solution, ψ, suitably scaled, is asymptotically equal to the solution of the TFW equation for an atom or molecule with electron repulsion in the regime where the nuclear charges are large and x is close to one of the nuclei.

Original languageEnglish (US)
Pages (from-to)15-25
Number of pages11
JournalCommunications In Mathematical Physics
Volume85
Issue number1
DOIs
StatePublished - Aug 1 1982

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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