Stability of Matter - From Atoms... | Buy

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.

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

(4)

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

Renormalization of the Regularized Electron-Positron Field

625

(12)

H. Siedentop

Ground States in Non-relativistic Quantum Electrodynamics

637

(42)

M. Griesemer

M. Loss

Part VIII. Bosonic Systems

Introduction

679

(2)

Ground State Energy of the Low Density Bose Gas

681

(4)

J. Yngvason

Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional

685

(14)

R. Seiringer

J. Yngvason

The Bose Gas: A Subtle Many-Body Problem

699

(22)

The N5/3 Law for Bosons

721

(4)

The N7/5 Law for Charged Bosons

725

(32)

J.G. Conlon

H.-T. Yau

Ground State Energy of the One-Component Charged Bose Gas

757

(38)

J.P. Solovej

Publications of Elliott H. Lieb

795

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