The Stability Of Matter From Atoms To Stars: Selecta Of Elliott H. Lieb

by Thirring, Walter E.; Lieb, Elliott H.; Thirring, Walter E.

• ISBN13: 9783540222125
• ISBN10: 354022212X
• Edition: 4th
• Format: Hardcover
• Copyright: 2004-10-16
• Publisher: Springer Verlag

Summary

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 own 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. Here 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 or recommended reading for a graduate course in quantum mechanics. In the third edition, two new sections were added: one contains papers on quantum electrodynamics, and the other on Boson systems. In this fourth edition, these topics have been further developed, extending the book by approximately 120 pages.

Table of Contents

Introduction	1	(10)
Part I. Review
The Stability of Matter: From Atoms to Stars	11	(52)
Part II. Exact Results on Atoms
Lower Bound to the Energy of Complex Atoms	63	(2)
P. Hertel
W. Thirring
Improved Lower Bound on the Indirect Coulomb Energy	65	(14)
S. Oxford
Monotonicity of the Molecular Electronic Energy in the Nuclear Coordinates	79	(4)
Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle	83	(4)
R. Benguria
Atomic and Molecular Negative Ions	87	(4)
Bound on the Maximum Negative Ionization of Atoms and Molecules	91	(12)
Approximate Neutrality of Large-Z Ions	103	(10)
I.M. Sigal
B. Simon
W. Thirring
Universal Nature of van der Waals Forces for Coulomb Systems	113	(8)
W. Thirring
Electron Density Near the Nucleus of a Large Atom	121	(6)
O.J. Heilmann
Proof of a Conjecture About Atomic and Molecular Cores Related to Scott's Correction	127	(20)
A. Iantchenko
H. Siedentop
Asymptotics of Natural and Artificial Atoms in Strong Magnetic Fields	147	(24)
J.P. Solovej
J. Yngvason
Ground States of Large Quantum Dots in Magnetic Fields	171	(22)
J.P. Solovej
J. Yngvason
Part III. General Results with Applications to Atoms
Kinetic Energy Bounds and Their Application to the Stability of Matter	193	(12)
Inequalities for the Moments of the Eigenvalues of the Schrodinger Hamiltonian and Their Relation to Sobolev Inequalities	205	(36)
W. Thirring
On Semi-Classical Bounds for Eigenvalues of Schrodinger Operators	241	(4)
M. Aizenman
The Number of Bound States of One-Body Schrodinger Operators and the Weyl Problem	245	(12)
Variational Principle for Many-Fermion Systems	257	(6)
Part IV. Thomas--Fermi and Related Theories
Thomas-Fermi and Related Theories of Atoms and Molecules	263	(40)
The Hartree--Fock Theory for Coulomb Systems	303	(10)
B. Simon
There Are No Unfilled Shells in Unrestricted Hartree--Fock Theory	313	(4)
V. Bach
M. Loss
J.P. Solovej
Many-Body Atomic Potentials in Thomas-Fermi Theory	317	(12)
R. Benguria
The Positivity of the Pressure in Thomas-Fermi Theory	329	(28)
R. Benguria
The Thomas--Fermi--von Weizsacker Theory of Atoms and Molecules	357	(14)
R. Benguria
H. Brezis
Analysis of the Thomas--Fermi--von Weizsacker Equation for an Infinite Atom Without Electron Repulsion	371	(12)
The Most Negative Ion in the Thomas--Fermi--von Weizsacker Theory of Atoms and Molecules	383	(18)
R. Benguria
Part V. Stability of Matter
Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter	401	(36)
W. Thirring
Stability of Coulomb Systems with Magnetic Fields
The One-Electron Atom	405	(20)
J. Frohlich
M. Loss
Stability of Coulomb Systems with Magnetic Fields
The Many-Electron Atom and the One-Electron Molecule	425	(12)
M. Loss
Stability of Matter in Magnetic Fields	437	(6)
M. Loss
J.P. Solovej
The Chandrasekhar Theory of Stellar Collapse as the Limit of Quantum Mechanics	443	(28)
H.-T. Yau
One-Electron Relativistic Molecules with Coulomb Interaction	471	(14)
I. Daubechies
The Stability and Instability of Relativistic Matter	485	(38)
H.-T. Yau
Stability of Relativistic Matter Via-Thomas--Fermi Theory	523	(12)
M. Loss
H. Siedentop
Stability and Instability of Relativistic Electrons in Classical Electromagnetic Fields	535	(26)
H. Siedentop
J.P. Solovej
Part VI. The Thermodynamic Limit for Real Matter with Coulomb Forces
The Stability of Matter	561	(18)
Existence of Thermodynamics for Real Matter with Coulomb Forces	579	(4)
J.L. Lebowitz
The Thermodynamic Limit for Jellium	583	(24)
H. Narnhofer
Part VII. Quantum Electrodynamics
Self Energy of Electrons in Non-perturbative QED	607	(18)
M. Loss
Ground-States in Non-relativistic Quantum Electrodynamics	625	(40)
M. Griesemer
M. Loss
Existence of Atoms and Molecules in Non-Relativistic Quantum Electrodynamics	665	(44)
M. Loss
A Bound on Binding Energies and Mass Renormalization in Models of Quantum Electrodynamics	709	(14)
M. Loss
Stability of a Model of Relativistic Quantum Electrodynamics	723	(30)
M. Loss
Part VIII. Bosonic Systems
Introduction	753	(2)
Ground State Energy of the Low Density Bose Gas	755	(4)
J. Yngvason
Bosons in a Trap: A Rigorous Derivation of the Gross--Pitaevskii Energy Functional	759	(14)
R. Seiringer
J. Yngvason
The N5/3 Law for Bosons	773	(4)
The N7/5 Law for Charged Bosons	777	(32)
J.G. Conlon
H.-T. Yau
Ground State Energy of the One-Component Charged Bose Gas	809	(40)
J.P. Solovej
Ground State Energy of the Two-Component Charged Bose Gas	849	(50)
J.P. Solovej
Proof of Bose-Einstein Condensation for Dilute Trapped Gases	899	(4)
R. Seiringer
Superfluidity in Dilute Trapped Bose Gases	903	(6)
R. Seiringer
J. Yngvason
One-Dimensional Bosons in Three-Dimensional Traps	909	(4)
R. Seiringer
J. Yngvason
Selecta of Elliott H. Lieb	913	(2)
Publications of Elliott H. Lieb	915