The Stability of Matter: From Atoms to Stars: Selecta of Elliott H. Lieb

Front Matter....Pages I-XIII
Introduction....Pages 1-8
Front Matter....Pages 9-9
The Stability of Matter: From Atoms to Stars....Pages 11-59
Front Matter....Pages 61-61
Lower bound to the energy of complex atoms....Pages 63-64
Improved Lower Bound on the Indirect Coulomb Energy....Pages 65-77
Monotonicity of the molecular electronic energy in the nuclear coordinates....Pages 79-82
Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle....Pages 83-86
Atomic and Molecular Negative Ions....Pages 87-89
Bound on the maximum negative ionization of atoms and molecules....Pages 91-101
Approximate Neutrality of Large- Z Ions....Pages 103-112
Universal nature of van der Waals forces for Coulomb systems....Pages 113-119
Electron density near the nucleus of a large atom....Pages 121-126
Proof of a conjecture about atomic and molecular cores related to Scott’s correction....Pages 127-145
Asymptotics of Natural and Artificial Atoms in Strong Magnetic Fields....Pages 147-169
Ground states of large quantum dots in magnetic fields....Pages 171-190
Front Matter....Pages 191-191
Kinetic Energy Bounds and Their Application to the Stability of Matter....Pages 193-204
Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities....Pages 205-239
On Semi-Classical Bounds for Eigenvalues of SchröDinger Operators....Pages 241-243
The Number of Bound States of One-Body Schroedinger Operators and the Weyl Problem....Pages 245-256
Variational Principle for Many-Fermion Systems....Pages 257-259
Front Matter....Pages 261-261
Thomas-fermi and related theories of atoms and molecules....Pages 263-301
Front Matter....Pages 261-261
The Hartree-Fock Theory for Coulomb Systems....Pages 303-312
There Are No Unfilled Shells in Unrestricted Hartree-Fock Theory....Pages 313-315
Many-Body Atomic Potentials in Thomas—Fermi Theory....Pages 317-328
The Positivity of the Pressure in Thomas Fermi Theory....Pages 329-354
The Thomas—Fermi—von Weizsäcker Theory of Atoms and Molecules....Pages 357-370
Analysis of the Thomas-Fermi-von Weizsäcker Equation for an Infinite Atom Without Electron Repulsion....Pages 371-381
The most negative ion in the Thomas—Fermi—von Weizsäcker theory of atoms and molecules....Pages 383-397
Front Matter....Pages 399-399
Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter....Pages 401-404
Stability of Coulomb Systems with Magnetic Fields....Pages 405-424
Stability of Coulomb Systems with Magnetic Fields....Pages 425-436
Stability of Matter in Magnetic Fields....Pages 437-441
The Chandrasekhar Theory of Stellar Collapse as the Limit of Quantum Mechanics....Pages 443-470
One-Electron Relativistic Molecules with Coulomb Interaction....Pages 471-484
The Stability and Instability of Relativistic Matter....Pages 485-521
Stability of Relativistic Matter via Thomas—Fermi Theory....Pages 523-533
Stability and Instability of Relativistic Electrons in Classical Electromagnetic Fields....Pages 535-557
Front Matter....Pages 559-559
The stability of matter....Pages 561-577
Existence of Thermodynamics for Real Matter with Coulomb Forces....Pages 579-582
The Thermodynamic Limit for Jellium....Pages 583-602
Front Matter....Pages 605-605
Self-Energy of Electrons in Non-Perturbative QED....Pages 607-623
Front Matter....Pages 605-605
Renormalization of the Regularized Relativistic Electron-Positron Field....Pages 625-635
Ground states in non-relativistic quantum electrodynamics....Pages 637-675
Front Matter....Pages 677-677
Bosonic Systems....Pages 679-680
Ground State Energy of the Low Density Bose Gas....Pages 681-684
Bosons in a trap: A rigorous derivation of the Gross-Pitaevskii energy functional....Pages 685-697
The Bose Gas: A Subtle Many-Body Problem....Pages 699-719
The N 5/3 Law For Bosons....Pages 721-723
The N 7/5 Law for Charged Bosons....Pages 725-756
Ground State Energy of the One-Component Charged Bose Gas....Pages 757-793
Back Matter....Pages 797-812