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

Contents......Page 13
Introduction......Page 16
Part I. Review......Page 24
I.1 The Stability of Matter: From Atoms to Stars......Page 25
Part II. Exact Results on Atoms......Page 74
II.1 Lower Bound to the Energy of Complex Atoms......Page 75
II.2 Improved Lower Bound on the Indirect Coulomb Energy......Page 77
II.3 Monotonicity of the Molecular Electronic Energy in the Nuclear Coordinates......Page 90
II.4 Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle......Page 94
II.5 Atomic and Molecular Negative Ions......Page 98
II.6 Bound on the Maximum Negative lonization of Atoms and Molecules......Page 101
II.7 Approximate Neutrality of Large-Z Ions......Page 112
II.8 Universal Nature of van der Waals Forces for Coulomb Systems......Page 122
II.9 Electron Density Near the Nucleus of a Large Atom......Page 129
II.10 Proof of a Conjecture About Atomic and Molecular Cores Related to Scott’s Correction......Page 135
II.11 Asymptotics of Natural and Artificial Atoms in Strong Magnetic Fields......Page 154
II.12 Ground States of Large Quantum Dots in Magnetic Fields......Page 177
Part III. General Results with Applications to Atoms......Page 197
III.1 Kinetic Energy Bounds and Their Application to the Stability of Matter......Page 198
III.2 Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities......Page 210
III.3 On Semi-Classical Bounds for Eigenvalues of Schrödinger Operators......Page 245
III.4 The Number of Bound States of One-Body Schrödinger Operators and the Weyl Problem......Page 248
III.5 Variational Principle for Many-Fermion Systems......Page 260
Part IV. Thomas–Fermi and Related Theories......Page 264
I. Introduction......Page 265
II. Thomas-Fermi Theory......Page 266
III. The “No-Binding” and Related Potential–Theoretic Theorems......Page 273
IV. Dependence of the Thomas–Fermi Energy on the Nuclear Coordinates......Page 277
V. Thomas–Fermi Theory as the Z → ∞ Limit of Quantum Theory......Page 282
VI. Thomas–Fermi–Dirac Theory......Page 287
VII. Thomas–Fermi–von Weizsäcker Theory......Page 290
VIII. Thomas–Fermi–Dirac–von Weizsäcker Theory......Page 300
References......Page 301
Index......Page 303
IV.2 The Hartree–Fock Theory for Coulomb Systems......Page 305
IV.3 There Are No Unfilled Shells in Unrestricted Hartree–Fock Theory......Page 315
IV.4 Many-Body Atomic Potentials in Thomas–Fermi Theory......Page 318
IV.5 The Positivity of the Pressure in Thomas–Fermi Theory......Page 330
IV.6 The Thomas–Fermi–von Weizsacker Theory of Atoms and Molecules......Page 357
IV.7 Analysis of the Thomas–Fermi–von Weizsacker Equation for an Infinite Atom Without Electron Repulsion......Page 371
IV.8 The Most Negative Ion in the Thomas–Fermi–von Weizsacker Theory of Atoms and Molecules......Page 382
Part V. Stability of Matter......Page 397
V.1 Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter......Page 398
I. The One-Electron Atom......Page 402
II. The Many-Electron Atom and the One-Electron Molecule......Page 422
V.4 Stability of Matter in Magnetic Fields......Page 434
V.5 The Chandrasekhar Theory of Stellar Collapse as the Limit of Quantum Mechanics......Page 439
V.6 One-Electron Relativistic Molecules with Coulomb Interaction......Page 467
V.7 The Stability and Instability of Relativistic Matter......Page 481
V.8 Stability of Relativistic Matter Via Thomas–Fermi Theory......Page 518
V.9 Stability and Instability of Relativistic Electrons in Classical Electromagnetic Fields......Page 529
Part VI. The Thermodynamic Limit for Real Matter with Coulomb Forces......Page 552
VI.1 The Stability of Matter......Page 553
VI.2 Existence of Thermodynamics for Real Matter with Coulomb Forces......Page 570
VI.3 The Thermodynamic Limit for Jellium......Page 574
Part VII. Quantum Electrodynamics......Page 595
VII.1 Self Energy of Electrons in Non-perturbative QED......Page 596
VII.2 Ground-States in Non-relativistic Quantum Electrodynamics......Page 613
VII.3 Existence of Atoms and Moleculesin Non-Relativistic Quantum Electrodynamics......Page 652
VII.4 A Bound on Binding Energies and Mass Renormalization in Models of Quantum Electrodynamics......Page 696
VII.5 Stability of a Model of Relativistic Quantum Electrodynamics......Page 709
Part VIII. Bosonic Systems......Page 737
VIII.1 Introduction......Page 738
VIII.2 Ground State Energy of the Low Density Bose Gas......Page 740
VIII.3 Bosons in a Trap: A Rigorous Derivation of the Gross–Pitaevskii Energy Functional......Page 744
VIII.4 The N[sup(5/3)] Law for Bosons......Page 757
VIII.5 The N[sup(7/5)] Law for Charged Bosons......Page 760
VIII.6 Ground State Energy of the One-Component Charged Bose Gas......Page 792
VIII.7 Ground State Energy of the Two-Component Charged Bose Gas......Page 831
VIII.8 Proof of Bose-Einstein Condensation for Dilute Trapped Gases......Page 881
VIII.9 Superfluidity in Dilute Trapped Bose Gases......Page 885
VIII.10 One-Dimensional Bosons in Three-Dimensional Traps......Page 891
Selecta of Elliott H. Lieb......Page 895
Publications of Elliott H. Lieb......Page 896