Quantum Mechanics in Hilbert Space (eBook)

Front Cover 1
Quantum Mechanics in Hilbert Space 4
Copyright Page 5
Contents 8
Preface to the Second Edition 16
Preface to the First Edition 18
List of Symbols 20
Introduction 24
Chapter I. Basic Ideas of Hilbert Space Theory 34
1. Vector Spaces 34
2. Euclidean (Pre-Hilbert) Spaces 41
3. Metric Spaces 48
4. Hilbert Space 53
5. Wave Mechanics of a Single Particle Moving in One Dimension 67
References for Further Study 79
Chapter II. Measure Theory and Hilbert Spaces of Functions 80
1. Measurable Spaces 81
2. Measures and Measure Spaces 89
3. Measurable and Integrable Functions 103
4. Spaces of Square-Integrable Functions 124
5. The Hilbert Space of Systems of n Different Particles in Wave Mechanics 142
6. Direct Sums and Tensor Products of Hilbert Spaces 155
7. The Two-Body Bound-State Problem with a Spherically Symmetric Potential 170
References for Further Study 194
Chapter III. Theory of Linear Operators in Hilbert Spaces 195
1. Linear and Antilinear Operators on Euclidean Spaces 195
2. Linear Operators in Hilbert Spaces 205
3. Orthogonal Projection Operators 220
4. Isometric and Unitary Transformations 235
5. Spectral Measures 249
6. The Spectral Theorem for Unitary and Self-Adjoint Operators 264
References for Further Study 279
Chapter IV. The Axiomatic Structure of Quantum Mechanics 280
1. Basic Concepts in the Quantum Theory of Measurement 280
2. Functions of Compatible Observables 292
3. The Schroedinger, Heisenberg, and Interaction Pictures 308
4. State Vectors and Observables of Compound Systems 324
5. Complete Sets of Observables 334
6. Canonical Commutation Relations 352
7. The General Formalism of Wave Mechanics 371
8. Completely Continuous Operators and Statistical Operators 398
References for Further Study 435
Chapter V. Quantum Mechanical Scattering Theory 437
1. Basic Concepts in Scattering Theory of Two Particles 437
2. General Time-Dependent Two-Body Scattering Theory 461
3. General Time-Independent Two-Body Scattering Theory 481
4. Eigenfunction Expansions in Two-Body Potential Scattering Theory 514
5. Green Functions in Potential Scattering 543
6. Distorted Plane Waves in Potential Scattering 566
7. Wave and Scattering Operators in Potential Scattering 592
8. Fundamental Concepts in Multichannel Scattering Theory 619
References for Further Study 653
Hints and Solutions to Exercises 654
References 692
Index 702