The Stability of Matter: From Atoms to Stars

Selecta of Elliott H. Lieb

  • Walter Thirring

Table of contents

  1. Front Matter
    Pages I-XI
  2. Introduction

    1. Walter Thirring
      Pages 1-8
  3. Review

    1. Front Matter
      Pages 9-9
    2. Elliott H. Lieb
      Pages 11-49
  4. Exact Results on Atoms

    1. Front Matter
      Pages 61-61
    2. Peter Hertel, Elliot H. Lieb, Walter Thirring
      Pages 63-64
    3. Elliott H. Lieb, Stephen Oxford
      Pages 65-77
    4. Elliott H. Lieb
      Pages 86-88
    5. Elliott H. Lieb, Israel M. Sigal, Barry Simon, Walter Thirring
      Pages 100-102
    6. Elliott H. Lieb, Israel M. Sigal, Barry Simon, Walter Thirring
      Pages 103-112
    7. Elliott H. Lieb, Walter E. Thirring
      Pages 113-119
    8. Ole J. Heilmann, Elliott H. Lieb
      Pages 120-125
    9. Alexei Iantchenko, Elliott H. Lieb, Heinz Siedentop
      Pages 126-144
    10. Elliott H. Lieb, Jan Philip Solovej, Jakob Yngvason
      Pages 145-167
    11. Elliott H. Lieb, Jan Philip Solovej, Jakob Yngvason
      Pages 168-187
  5. General Results with Applications to Atoms

    1. Front Matter
      Pages 189-189

About this book

Introduction

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,

Keywords

Boson System Mathematische Methoden Mathematische Physik QED Thermodynamic Limit Thomas-Fermi Theory functional analysis quantum mechanics

Editors and affiliations

  • Walter Thirring
    • 1
  1. 1.Institut für Theoretische PhysikUniversität WienWienAustria

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03436-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-03438-5
  • Online ISBN 978-3-662-03436-1
  • About this book