An exact result for the Thomas-Fermi equation: A priori bounds for the potential slope at the origin

R. Iacono

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Abstract

We examine the nonlinear boundary value problem formed by the Thomas-Fermi equation ″ = 3/2x-1/2, complemented with the boundary conditions (0) = 1 and (∞) = 0. We show that the value of ′ at the origin, which plays a crucial role in this problem, can be accurately bounded a priori, by exploiting integral properties of the Thomas-Fermi equation, and without any assumption on the functional dependence of (x). Extension of the approach to more general equations of the Emden-Fowler type is also briefly considered. © 2008 IOP Publishing Ltd.
Original languageEnglish
Article number455204
Pages (from-to)-
JournalJournal of Physics A: Mathematical and Theoretical
Volume41
Issue number45
DOIs
Publication statusPublished - 14 Nov 2008
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Modelling and Simulation
  • Statistics and Probability
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

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