Book contents
- Frontmatter
- Contents
- Preface
- 1 The Quantum World and Its Description
- 2 Matter and Field
- 3 Quantum Mechanics in the Heisenberg (Matrix) Picture
- 4 Quantum Mechanics in the Schrödinger (Wave) Picture. Dirac‘s Notation
- 5 One-Dimensional Potential Steps, Barriers, and Wells
- 6 The WKB Approximation. Electronic Properties of Solids
- 7 The Free Particle. The Time-Dependent Schrödinger Equation
- 8 Dynamics of Quantum Systems
- 9 The One-Dimensional Harmonic Oscillator
- 10 The Physics Underlying Quantum Phenomena
- 11 Angular Momentum Theory
- 12 Central Potentials. The Hydrogen Atom
- 13 Stationary Perturbation Theory and the Variational Method
- 14 The Electron Spin. Entangled States
- 15 Identical-Particle Systems: Quantum Statistics. The Density Matrix
- 16 Atoms and Molecules
- 17 Time-Dependent Perturbations. Field Quantization and Second Quantization
- 18 Elastic Scattering Theory
- 19 Relativistic Equations. An Introduction
- Appendix A Mathematical Tools
- References
- Index
15 - Identical-Particle Systems: Quantum Statistics. The Density Matrix
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Book contents
- Frontmatter
- Contents
- Preface
- 1 The Quantum World and Its Description
- 2 Matter and Field
- 3 Quantum Mechanics in the Heisenberg (Matrix) Picture
- 4 Quantum Mechanics in the Schrödinger (Wave) Picture. Dirac‘s Notation
- 5 One-Dimensional Potential Steps, Barriers, and Wells
- 6 The WKB Approximation. Electronic Properties of Solids
- 7 The Free Particle. The Time-Dependent Schrödinger Equation
- 8 Dynamics of Quantum Systems
- 9 The One-Dimensional Harmonic Oscillator
- 10 The Physics Underlying Quantum Phenomena
- 11 Angular Momentum Theory
- 12 Central Potentials. The Hydrogen Atom
- 13 Stationary Perturbation Theory and the Variational Method
- 14 The Electron Spin. Entangled States
- 15 Identical-Particle Systems: Quantum Statistics. The Density Matrix
- 16 Atoms and Molecules
- 17 Time-Dependent Perturbations. Field Quantization and Second Quantization
- 18 Elastic Scattering Theory
- 19 Relativistic Equations. An Introduction
- Appendix A Mathematical Tools
- References
- Index
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Summary
Chapter 15 is devoted to systems of identical particles and the associated quantum statistics. It is shown how the spin (whether integer or half-integer) determines fundamental features of the system’s behavior that cannot be obtained by approximate methods, in particular the exchange effects characteristic of states of two or more identical particles. The spin-symmetry relation is discussed in detail for both the Bose–Einstein and the Fermi–Dirac statistics. Quantum collective phenomena that are a defining feature of condensed matter, including phonons, superconductivity, Bose–Einstein condensates and the quantum Hall effect, are briefly introduced. Since most real quantum systems consist of subsystems in different quantum states that are mixtures of pure states, the chapter includes an introduction to the density matrix, its basic properties and its application to quantum statistics. It concludes with a critical discussion of decoherence and the significance of the collapse of the wave function.
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- Quantum MechanicsA Physical Approach, pp. 392 - 436Publisher: Cambridge University PressPrint publication year: 2025
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