Book contents
- Frontmatter
- Contents
- Preface
- 1The Quantum World and Its Description
- 2Matter and Field
- 3Quantum Mechanics in the Heisenberg (Matrix) Picture
- 4Quantum Mechanics in the Schrödinger (Wave) Picture. Dirac‘s Notation
- 5One-Dimensional Potential Steps, Barriers, and Wells
- 6The WKB Approximation. Electronic Properties of Solids
- 7The Free Particle. The Time-Dependent Schrödinger Equation
- 8Dynamics of Quantum Systems
- 9The One-Dimensional Harmonic Oscillator
- 10The Physics Underlying Quantum Phenomena
- 11Angular Momentum Theory
- 12Central Potentials. The Hydrogen Atom
- 13Stationary Perturbation Theory and the Variational Method
- 14The Electron Spin. Entangled States
- 15Identical-Particle Systems: Quantum Statistics. The Density Matrix
- 16Atoms and Molecules
- 17Time-Dependent Perturbations. Field Quantization and Second Quantization
- 18Elastic Scattering Theory
- 19Relativistic Equations. An Introduction
- Appendix AMathematical Tools
- References
- Index
18 - Elastic Scattering Theory
Published online by Cambridge University Press: 27 December 2025
Book contents
- Frontmatter
- Contents
- Preface
- 1The Quantum World and Its Description
- 2Matter and Field
- 3Quantum Mechanics in the Heisenberg (Matrix) Picture
- 4Quantum Mechanics in the Schrödinger (Wave) Picture. Dirac‘s Notation
- 5One-Dimensional Potential Steps, Barriers, and Wells
- 6The WKB Approximation. Electronic Properties of Solids
- 7The Free Particle. The Time-Dependent Schrödinger Equation
- 8Dynamics of Quantum Systems
- 9The One-Dimensional Harmonic Oscillator
- 10The Physics Underlying Quantum Phenomena
- 11Angular Momentum Theory
- 12Central Potentials. The Hydrogen Atom
- 13Stationary Perturbation Theory and the Variational Method
- 14The Electron Spin. Entangled States
- 15Identical-Particle Systems: Quantum Statistics. The Density Matrix
- 16Atoms and Molecules
- 17Time-Dependent Perturbations. Field Quantization and Second Quantization
- 18Elastic Scattering Theory
- 19Relativistic Equations. An Introduction
- Appendix AMathematical Tools
- References
- Index
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Summary
Chapter 18 is entirely devoted to the quantum theory of scattering, which is normally covered in more detail in a course on quantum field theory. We introduce the main concepts, including scattering amplitude, differential and total cross sections, and form factors, and derive the main formulas for elastic scattering, in a nonrelativistic framework; this allows us to appreciate how the information obtained from scattering experiments is used to explore the intricacies of quantum particles that are otherwise inaccessible. The Born approximation is studied and applied to scattering by a periodic potential, a weak potential, and Rutherford scattering. The partial wave expansion is derived and applied to obtain the optical theorem. The chapter concludes with a complementary section on resonant scattering.
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- Information
- Quantum MechanicsA Physical Approach, pp. 531 - 560Publisher: Cambridge University PressPrint publication year: 2025
- Creative Commons
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