E-Book Overview
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 own 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. Here 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 or recommended reading for a graduate course in quantum mechanics. In the third edition, two new sections were added: one contains papers on quantum electrodynamics, and the other on Boson systems. In this fourth edition, these topics have been further developed, extending the book by approximately 120 pages.
E-Book Information
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Year: 2,005
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Edition: 4
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Pages: 932
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Pages In File: 903
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Language: English
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Identifier: 978-3-540-22212-5,978-3-540-27056-0
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Doi: 10.1007/b138553
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Cleaned: 1
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Orientation: 1
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Paginated: 1
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Org File Size: 63,241,525
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Extension: pdf
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Tags: Mathematical Methods in Physics Condensed Matter Quantum Physics Analysis Calculus of Variations and Optimal Control Optimization
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Toc: Introduction....Pages 1-8The Stability of Matter: From Atoms to Stars....Pages 11-59Lower bound to the energy of complex atoms....Pages 63-64Improved Lower Bound on the Indirect Coulomb Energy....Pages 65-77Letter to the Editor....Pages 79-82Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle....Pages 83-86Atomic and Molecular Negative Ions....Pages 87-89Bound on the maximum negative ionization of atoms and molecules....Pages 91-101Approximate Neutrality of Large- Z Ions....Pages 103-112Universal nature of van der Waals forces for Coulomb Systems....Pages 113-119Electron density near the nucleus of a large atom....Pages 121-126Proof of a conjecture about atomic and molecular cores related to Scott’s correction....Pages 127-145Asymptotics of Natural and Artificial Atoms in Strong Magnetic Fields....Pages 147-169Ground states of large quantum dots in magnetic fields....Pages 171-190Kinetic Energy Bounds and Their Application to the Stability of Matter....Pages 193-204Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities....Pages 205-239On Semi-Classical Bounds for Eigenvalues of Schrödinger Operators....Pages 241-243The Number of Bound States of One-Body Schroedincer Operators and the Weyl Problem....Pages 245-256Variational Principle for Many-Fermion Systems....Pages 257-260Thomas