Skip to main content
SpringerLink
Log in

The Stability of Matter: From Atoms to Stars

Selecta of Elliot H. Lieb

  • Book
  • © 1997

Overview

Editors:
  1. Walter Thirring

    1. Institut für Theoretische Physik, Universität Wien, Wien, Austria

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (51 chapters)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  2. Introduction

    1. Introduction

      • Walter Thirring
      Pages 1-8

  3. Review

    1. Front Matter

      Pages 9-9
      Download chapter PDF

    2. The Stability of Matter: From Atoms to Stars

      • Elliott H. Lieb
      Pages 11-49

  4. Exact Results on Atoms

    1. Front Matter

      Pages 61-61
      Download chapter PDF

    2. Lower bound to the energy of complex atoms

      • Peter Hertel, Elliot H. Lieb, Walter Thirring
      Pages 63-64

    3. Improved Lower Bound on the Indirect Coulomb Energy

      • Elliott H. Lieb, Stephen Oxford
      Pages 65-77

    4. Monotonicity of the molecular electronic energy in the nuclear coordinates

      • Elliott H. Lieb
      Pages 78-81

    5. Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle

      • Rafael Benguria, Elliott H. Lieb
      Pages 82-85

    6. Atomic and Molecular Negative Ions

      • Elliott H. Lieb
      Pages 86-88

    7. Bound on the maximum negative ionization of atoms and molecules

      • Elliott H. Lieb
      Pages 89-99

    8. Asymptotic Neutrality of Large-Z Ions

      • Elliott H. Lieb, Israel M. Sigal, Barry Simon, Walter Thirring
      Pages 100-102

    9. Approximate Neutrality of Large-Z Ions

      • Elliott H. Lieb, Israel M. Sigal, Barry Simon, Walter Thirring
      Pages 103-112

    10. Universal nature of van der Waals forces for Coulomb systems

      • Elliott H. Lieb, Walter E. Thirring
      Pages 113-119

    11. Electron density near the nucleus of a large atom

      • Ole J. Heilmann, Elliott H. Lieb
      Pages 120-125

    12. Proof of a conjecture about atomic and molecular cores related to Scott’s correction

      • Alexei Iantchenko, Elliott H. Lieb, Heinz Siedentop
      Pages 126-144

    13. Asymptotics of Natural and Artificial Atoms in Strong Magnetic Fields

      • Elliott H. Lieb, Jan Philip Solovej, Jakob Yngvason
      Pages 145-167

    14. Ground states of large quantum dots in magnetic fields

      • Elliott H. Lieb, Jan Philip Solovej, Jakob Yngvason
      Pages 168-187

  5. General Results with Applications to Atoms

    1. Front Matter

      Pages 189-189
      Download chapter PDF

    2. Kinetic Energy Bounds and Their Application to the Stability of Matter

      • Elliott H. Lieb
      Pages 191-202
Back to top

Keywords

About this book

The first edition of "The Stability of Matter: From Atoms to Stars" was sold out after a time unusually short for a selecta collection and we thought it ap­ propriate not just to make a reprinting but to include eight new contributionso They demonstrate that this field is still lively and keeps revealing unexpected featureso Of course, we restricted ourselves to developments in which Elliott Lieb participated and thus the heroic struggle in Thomas-Fermi theory where 7 3 5 3 the accuracy has been pushed from Z 1 to Z 1 is not includedo A rich landscape opened up after Jakob Yngvason's observation that atoms in magnetic fields also are described in suitable limits by a Thomas-Fermi-type theoryo Together with Elliott Lieb and Jan Philip Solovej it was eventually worked out that one has to distinguish 5 regionso If one takes as a dimensionless measure of the magnetic field strength B the ratio Larmor radius/Bohr radius one can compare it with N "' Z and for each of the domains 4 3 (i) B « N 1 , 4 3 (ii) B "' N 1 , 4 3 3 (iii) N 1« B « N , 3 (iv) B "' N , 3 (v) B » N a different version ofmagnetic Thomas-Fermi theory becomes exact in the limit N --+ ooo In two dimensions and a confining potential ("quantum dots") the situation is somewhat simpler, one has to distinguish only (i) B « N, (ii) B "'N,

Editors and Affiliations

  • Institut für Theoretische Physik, Universität Wien, Wien, Austria

    Walter Thirring

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation