© 2001

The Stability of Matter: From Atoms to Stars

Selecta of Elliott H. Lieb

  • Walter Thirring
  • Elliott H. Lieb has been awarded the Rolf Schock Prize in Mathematics of the Swedish Academy of Sciences for 2001 for his outstanding work in mathematical physics, particularly for his contribution to the mathematical understanding of the quantum-mechanical many-body theory and for his work on exact solutions of models in statistical mechanics and quantum mechanics


Table of contents

  1. Front Matter
    Pages I-XIII
  2. Introduction

    1. Walter Thirring
      Pages 1-8
  3. Review

    1. Front Matter
      Pages 9-9
    2. Elliott H. Lieb
      Pages 11-59
  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 87-89
    5. Elliott H. Lieb, Israel M. Sigal, Barry Simon, Walter Thirring
      Pages 103-112
    6. Elliott H. Lieb, Walter E. Thirring
      Pages 113-119
    7. Ole J. Heilmann, Elliott H. Lieb
      Pages 121-126
    8. Alexei Iantchenko, Elliott H. Lieb, Heinz Siedentop
      Pages 127-145
    9. Elliott H. Lieb, Jan Philip Solovej, Jakob Yngvason
      Pages 147-169
    10. Elliott H. Lieb, Jan Philip Solovej, Jakob Yngvason
      Pages 171-190
  5. General Results with Applications to Atoms

About this book


This collection of papers -- starting with a brilliant article by one of the masters of the field -- gives an excellent current review of our knowledge of matter. Partially basing his work on a variational formulation of quantum mechanics, E.H. Lieb links the difficult question of the stability of matter with important problems in functional analysis. In this collection the reader will find general results together with deep insights into quantum systems combined with papers on the structure of atoms and molecules, the thermodynamic limit, and stellar structures. The book is suitable as an accompanying text for a graduate course in quantum mechanics. In this new edition two new sections have been added: Section 7 contains papers on quantum electrodynamics, and Section 8 on Boson systems. .


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

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 From the reviews:

"The rapid soldout of the two previous editions by itself demonstrates the high value of this book. The reader will have indeed the opportunity to gaze on the formidable mastering of functional analysis by Elliot Lieb and to discover mathematical and Physical depths in the description of, after all, familar physical phenomena. [...] The third edition contains new developments compared to previous ones, witnessing that the field is still lively. In particular there are important results concerning systems of bosons. [...] In conclusion, this book is a delight for readers interested in the stability and related properties of many-body systems. It, moreover, offers the oppertunity to admire the elegant mathematical considerations and the penetrating physical insight of a great theoretician." (Physicalia, 2002)