Quantum Mathematical Physics

by Thirring, Walter E.; Harrell, Evans M., II

• ISBN13: 9783540430780
• ISBN10: 3540430784
• Edition: 2nd
• Format: Hardcover
• Copyright: 2002-10-01
• Publisher: Springer Verlag

Summary

This book is a new edition of Volumes 3 and 4 of Walter Thirring's famous textbook on mathematical physics. The first part is devoted to quantum mechanics and especially to its applications to scattering theory, atoms and molecules. The second part deals with quantum statistical mechanics examining fundamental concepts like entropy, ergodicity and thermodynamic functions. The author builds on an axiomatic basis and uses tools from functional analysis: bounded and unbounded operators on Hilbert space, operator algebras etc. Mathematics is shown to explain the axioms in depth and to provide the right tool for testing numerical data in experiments.

Table of Contents

Preface	v
Preface to the Second Edition: Quantum Mechanics of Atoms and Molecules	vii
Preface to the First Edition: Quantum Mechanics of Atoms and Molecules	xi
Preface to the First Edition: Quantum Mechanics of Large Systems	xi
Symbols Defined in the Text	xv
I Quantum Mechanics of Atoms and Molecules	1	(280)
Introduction	3	(8)
The Structure of Quantum Theory	3	(2)
The Orders of Magnitude of Atomic Systems	5	(6)
The Mathematical Formulation of Quantum Mechanics	11	(74)
Linear Spaces	11	(12)
Algebras	23	(17)
Representations on Hilbert Space	40	(15)
One-Parameter Groups	55	(13)
Unbounded Operators and Quadratic Forms	68	(17)
Quantum Dynamics	85	(100)
The Weyl System	85	(11)
Angular Momentum	96	(9)
Time-Evolution	105	(17)
The Limit t → ± ∞	122	(19)
Perturbation Theory	141	(21)
Stationary Scattering Theory	162	(23)
Atomic Systems	185	(96)
The Hydrogen Atom	185	(14)
The Hydrogen Atom in an External Field	199	(11)
Helium-like Atoms	210	(29)
Scattering Theory of Simple Atoms	239	(15)
Complex Atoms	254	(12)
Nuclear Motion and Simple Molecules	266	(15)
II Quantum Mechanics of Large Systems	281	(288)
Systems with Many Particles	283	(44)
Equilibrium and Irreversibility	283	(10)
The Limit of an Infinite Number of Particles	293	(9)
Arbitrary Numbers of Particles in Fock Space	302	(10)
Representations with N = ∞	312	(15)
Thermostatics	327	(96)
The Ordering of the States	327	(12)
The Properties of Entropy	339	(13)
The Microcanonical Ensemble	352	(30)
The Canonical Ensemble	382	(14)
The Grand Canonical Ensemble	396	(27)
Thermodynamics	423	(78)
Time-Evolution	423	(29)
The Equilibrium State	452	(18)
Stability and Passivity	470	(16)
Quantum Ergodic Theory	486	(15)
Physical Systems	501	(68)
Thomas-Fermi Theory	501	(33)
Cosmic Bodies	534	(14)
Normal Matter	548	(21)
Bibliography	569	(10)
Index	579