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Analysis of the Thomas-Fermi-von Weizsäcker Equation for an Infinite Atom Without Electron Repulsion

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Book cover The Stability of Matter: From Atoms to Stars

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Abstract

The equation

$$ \left\{ { - \vartriangle + {{\left| {\psi \left( x \right)} \right|}^{2p - 2}} - {{\left| x \right|}^{ - 1}}} \right\}\psi (x) = 0 $$

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.

Work partially supported by U.S. National Science Foundation grant PHY-7825390 A02

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Author information

Authors and Affiliations

  1. Departments of Mathematics and Physics, Princeton University, P.O.B. 708, Princeton, NJ, 08544, USA

    Elliott H. Lieb

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  1. Elliott H. Lieb
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Editors and Affiliations

  1. Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, A-1090, Wien, Austria

    Walter Thirring

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© 1997 Springer-Verlag Berlin Heidelberg

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Lieb, E.H. (1997). Analysis of the Thomas-Fermi-von Weizsäcker Equation for an Infinite Atom Without Electron Repulsion. In: Thirring, W. (eds) The Stability of Matter: From Atoms to Stars. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03436-1_31

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  • DOI: https://doi.org/10.1007/978-3-662-03436-1_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-03438-5

  • Online ISBN: 978-3-662-03436-1

  • eBook Packages: Springer Book Archive

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