The stability of matter in quantum mechanics
By: Elliott H Lieb, Robert Seiringer.
Contributors: Seiringer, Robert.
Publisher: Cambridge University Press
Published: 2010
Place of publication: New York
Language: eng
Number of pages: 293
ISBN-13: 9780521191180
Subjects: Thomas-Fermi theory; Quantum theory; Matter -- Properties; Structural stability
Description: "Research into the stability of matter has been one of the most successful chapters in mathematical physics, and is a prime example of how modern mathematics can be applied to problems in physics. A unique account of the subject, this book provides a complete, self-contained description of research on the stability of matter problem. It introduces the necessary quantum mechanics to mathematicians, and aspects of functional analysis to physicists. The topics covered include electrodynamics of classical and quantized fields, Lieb-Thirring and other inequalities in spectral theory, inequalities in electrostatics, stability of large Coulomb systems, gravitational stability of stars, basics of equilibrium statistical mechanics, and the existence of the thermodynamic limit. The book is an up-to-date account for researchers, and its pedagogical style makes it suitable for advanced undergraduate and graduate courses in mathematical physics"--Provided by publisher.

"Despite the great success of quantum mechanics in explaining details of the structure of atoms, molecules (including the complicated molecules beloved of organic chemists and the pharmaceutical industry, and so essential to life) and macroscopic objects like transistors, it took 41 years before the most fundamental question of all was resolved: Why doesn't the collection of negatively charged electrons and positively charged nuclei, which are the basic constituents of the theory, implode into a minuscule mass of amorphous matter thousands of times denser than the material normally seen in our world? It is this stability question that will occupy us in this book. After four decades of development of this subject, during which most of the basic questions have gradually been answered, it seems appropriate to present a thorough review of the material at this time"--Provided by publisher.
Notes: Includes bibliographical references and index.
Table of contents: title: Machine generated contents note: Preface; 1. Prologue; 2. Introduction to elementary quantum mechanics and stability of the first kind; 3. Many-particle systems and stability of the second kind; 4. Lieb-Thirring and related inequalities; 5. Electrostatic inequalities; 6. An estimation of the indirect part of the coulomb energy; 7. Stability of non-relativistic matter; 8. Stability of relativistic matter; 9. Magnetic fields and the Pauli operator; 10. The Dirac operator and the Brown-Ravenhall model; 11. Quantized electromagnetic fields and stability of matter; 12. The ionization problem, and the dependence of the energy on N and M separately; 13. Gravitational stability of white dwarfs and neutron stars; 14. The thermodynamic limit for coulomb systems; References; Index.