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

Front Matter....Pages I-XI
Introduction....Pages 1-8
Front Matter....Pages 9-9
The Stability of Matter: From Atoms to Stars....Pages 11-49
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 78-81
Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle....Pages 82-85
Atomic and Molecular Negative Ions....Pages 86-88
Bound on the maximum negative ionization of atoms and molecules....Pages 89-99
Asymptotic Neutrality of Large- Z Ions....Pages 100-102
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 120-125
Proof of a conjecture about atomic and molecular cores related to Scott’s correction....Pages 126-144
Asymptotics of Natural and Artificial Atoms in Strong Magnetic Fields....Pages 145-167
Ground states of large quantum dots in magnetic fields....Pages 168-187
Front Matter....Pages 189-189
Kinetic Energy Bounds and Their Application to the Stability of Matter....Pages 191-202
Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities....Pages 203-237
On Semi-Classical Bounds for Eigenvalues of Schrödinger Operators....Pages 238-240
The Number of Bound States of One-Body Schroedinger Operators and the Weyl Problem....Pages 241-252
Variational Principle for Many-Fermion Systems....Pages 253-255
Front Matter....Pages 189-189
Erratum to: Variational Principle for Many-Fermion Systems....Pages 256-256
Front Matter....Pages 391-391
Thomas-fermi and related theories of atoms and molecules....Pages 259-297
Erratum to: Thomas-fermi and related theories of atoms and molecules....Pages 298-298
Erratum to: Thomas-fermi and related theories of atoms and molecules....Pages 298-298
The Hartree-Fock Theory for Coulomb Systems....Pages 299-308
There Are No Unfilled Shells in Unrestricted Hartree-Fock Theory....Pages 309-311
Many-Body Atomic Potentials in Thomas-Fermi Theory....Pages 312-323
The Positivity of the Pressure in Thomas Fermi Theory....Pages 324-349
Erratum to: The Positivity of the Pressure in Thomas Fermi Theory....Pages 350-350
The Thomas—Fermi—von Weizsäcker Theory of Atoms and Molecules....Pages 351-364
Analysis of the Thomas-Fermi-von Weizsäcker Equation for an Infinite Atom Without Electron Repulsion....Pages 365-375
The most negative ion in the Thomas—Fermi—von Weizsäcker theory of atoms and molecules....Pages 376-390
Front Matter....Pages 391-391
Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter....Pages 393-396
Erratum to: Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter....Pages 396-396
The N 5/3 Law for Bosons....Pages 397-399
Stability of Coulomb Systems with Magnetic Fields....Pages 400-419
Stability of Coulomb Systems with Magnetic Fields....Pages 420-431
Stability of Matter in Magnetic Fields....Pages 432-436
A Rigorous Examination of the Chandrasekhar Theory of Stellar Collapse....Pages 437-441
The Chandrasekhar Theory of Stellar Collapse as the Limit of Quantum Mechanics....Pages 442-469
Front Matter....Pages 391-391
One-Electron Relativistic Molecules with Coulomb Interaction....Pages 470-483
Many-Body Stability Implies a Bound on the Fine-Structure Constant....Pages 484-486
The Stability and Instability of Relativistic Matter....Pages 487-523
Stability of Relativistic Matter via Thomas-Fermi Theory....Pages 524-534
Stability and Instability of Relativistic Electrons in Classical Electromagnetic Fields....Pages 535-555
The N 7/5 Law for Charged Bosons....Pages 556-587
Front Matter....Pages 589-589
The stability of matter....Pages 591-607
Existence of Thermodynamics for Real Matter with Coulomb Forces....Pages 608-611
Lectures on the Thermodynamic Limit for Coulomb Systems....Pages 612-637
The Thermodynamic Limit for Jellium....Pages 638-657
Erratum to: The Thermodynamic Limit for Jellium....Pages 658-658
Back Matter....Pages 659-676