Some model inhomogeneous electron liquid in D dimensions: Relation between energy and chemical potential and a spatial generalisation of Kato's nuclear cusp theorem

N. H. March, A. Nagy

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

After a brief survey on the application of the Thomas-Fermi statistical method to bare Coulomb potential satisfying Laplace equation in D dimensions, which then relates energy and chemical potential, we next focus attention on model atomic ions with merely one and two electrons in D dimensions. In particular, for a bare Coulomb field we use the nodeless radial eigenfunctions given by Herschbach in D dimensions to derive the spatial generalization of Kato's nuclear cusp theorem in D dimensions for D > 1. The unbinding of H - as a function of dimensionality D is also briefly referred.

Original languageEnglish
Pages (from-to)266-270
Number of pages5
JournalPhysics and Chemistry of Liquids
Volume50
Issue number2
DOIs
Publication statusPublished - Mar 2012

Fingerprint

Laplace equation
Chemical potential
cusps
Eigenvalues and eigenfunctions
Statistical methods
theorems
Ions
Electrons
Liquids
liquids
electrons
energy
Coulomb potential
eigenvectors
ions

Keywords

  • cusp condition in bare Coulomb field
  • electron liquid in D dimension
  • generalization of Kato's theorem

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Materials Chemistry
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry

Cite this

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AB - After a brief survey on the application of the Thomas-Fermi statistical method to bare Coulomb potential satisfying Laplace equation in D dimensions, which then relates energy and chemical potential, we next focus attention on model atomic ions with merely one and two electrons in D dimensions. In particular, for a bare Coulomb field we use the nodeless radial eigenfunctions given by Herschbach in D dimensions to derive the spatial generalization of Kato's nuclear cusp theorem in D dimensions for D > 1. The unbinding of H - as a function of dimensionality D is also briefly referred.

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