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

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概要 With this book, Elliott Lieb joins his peers Hermann Weyl and Chen Ning Yang. Weyl's Selecta was published in 1956, Yang's Selected Papers in 1983. Lieb's "Selecta", like its predecessors, gives us th...e essence of a great mathema tical physicist concentrated into one convenient volume. Weyl, Yang and Lieb have much more in common than the accident of this manner of publication. They have in common a style and a tradition. Each of them is master of a for midable mathematical technique. Each of them uses hard mathematical ana lysis to reach an understanding of physical laws. Each of them enriches both physics and mathematics by finding new mathematical depths in the description of familiar physical processes. The central theme of Weyl's work in mathematical physics was the idea of symmetry, linking physical invariance-principles with the mathematics of group-theory. One of Yang's central themes is the idea of a gauge field, linking physical interactions with the mathematics of fibre-bundles. The central theme of Lieb's papers collected in this book is the classical Thomas-Fermi model of an atom, linking the physical stability of matter with the mathematics of func tional analysis. In all three cases, a rather simple physical idea provided the starting-point for building a grand and beautiful mathematical structure. Weyl, Yang and Lieb were not content with merely solving a problem. Each of them was concerned with understanding the deep mathematical roots out of which physical phenomena grow.続きを見る
目次 I. Review
I.1 The Stability of Matter: From Atoms to Stars
II. Exact Results on Atoms
II.1 Lower Bound to the Energy of Complex Atoms
II.2 Improved Lower Bound on the Indirect Coulomb Energy
II.3 Monotonicity of the Molecular Electronic Energy in the Nuclear Coordinates
II.4 Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle
II.5 Atomic and Molecular Negative Ions
II.6 Bound on the Maximum Negative Ionization of Atoms and Molecules
II.7 Asymptotic Neutrality of Large-Z Ions
II.8 Universal Nature of van der Waals Forces for Coulomb Systems
II.9 Approximate Neutrality of Large-Z Ions
III. General Results with Applications to Atoms
III.1 Kinetic Energy Bounds and Their Application to the Stability of Matter
III.2 Inequalities for the Moments of the Eigenvalues of the Schrodinger Hamiltonian and Their Relation to Sobolev Inequalities
III.3 On Semi-Classical Bounds for Eigenvalues of Schrodinger Operators
III.4 The Number of Bound States of One-Body Schrodinger Operators and the Weyl Problem
111.5 Variational Principle for Many-Fermion Systems
IV. Thomas-Fermi and Related Theories
IV.1 Thomas-Fermi and Related Theories of Atoms and Molecules
IV.2 The Hartree-Fock Theory for Coulomb Systems
IV.3 Many-Body Atomic Potentials in Thomas-Fermi Theory
IV.4 The Positivity of the Pressure in Thomas-Fermi Theory
IV.5 The Thomas-Fermi-von Weizsäcker Theory of Atoms and Molecules
IV.6 Analysis of the Thomas-Fermi-von Weizsäcker Equation for an Infinite Atom Without Electron Repulsion
IV.7 The Most Negative Ion in the Thomas-Fermi-von Weizsäcker Theory of Atoms and Molecules
V. Stability of Matter
V.1 Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter
V.2 The N5/3 Law for Bosons
V.3 Stability of Coulomb Systems with Magnetic Fields. I. The One-Electron Atom
V.4 Stability of Coulomb Systems with Magnetic Fields. II. The Many-Electron Atom and the One-Electron Molecule
V.5 The Chandrasekhar Theory of Stellar Collapse as the Limit of Quantum Mechanics
V.6 A Rigorous Examination of the Chandrasekhar Theory of Stellar Collapse
V.7 The Stability and Instability of Relativistic Matter
V.8 Many-Body Stability Implies a Bound on the Fine-Structure Constant
V.9 The N7/5 Law for Charged Bosons
V.10 One-Electron Relativistic Molecules with Coulomb Interaction
VI. The Thermodynamic Limit for Real Matter with Coulomb Forces
VI.1 The Stability of Matter
VI.2 Existence of Thermodynamics for Real Matter with Coulomb Forces
VI.3 Lectures on the Thermodynamic Limit for Coulomb Systems
VI.4 The Thermodynamic Limit for Jellium
Publications of Elliott H. Lieb.
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登録日 2020.06.27
更新日 2020.06.28