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
8 - Dynamics of Quantum Systems
Published online by Cambridge University Press: 27 December 2025
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 8 is devoted to the study of the dynamics of quantum systems, based on the formalism presented in Chapter 7 and previous chapters. The operator notation and its matrix representation are used without distinction, moving freely from one to the other as convenient. This allows us to study the evolution of the system from different perspectives, depending on the description adopted. The chapter includes a discussion of the statistical information contained in the quantum formalism, a formal derivation of the Heisenberg inequalities and a clarification of their physical meaning. A section is dedicated to quantum canonical and related transformations. More advanced topics, which provide a valuable complement, include Noether’s theorem on the relationship between the symmetry properties and the conserved dynamical variables of the system.
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- Quantum MechanicsA Physical Approach, pp. 191 - 221Publisher: Cambridge University PressPrint publication year: 2025
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