Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- 1 The Failure of Classical Physics
- 2 Wave–Particle Duality andWave Mechanics
- 3 Schrödinger Equation; Uncertainty Relations
- 4 The One-Dimensional Schrödinger Equation; Bound States
- 5 Scattering in One Dimension
- 6 Mathematical Formulation of Quantum Mechanics
- 7 Physical Interpretation: Postulates of Quantum Mechanics
- 8 The Harmonic Oscillator
- 9 Particle in a Central Potential; Orbital Angular Momentum
- 10 Bound States in a Central Potential: Applications
- 11 Angular Momentum: General Properties
- 12 Spin; Charged Particle in an Electromagnetic Field
- 13 Addition of Angular Momenta
- 14 Approximation Methods
- 15 Scattering by a Potential
- 16 Symmetry Transformations of States and Operators
- 17 Rotation Matrices and the Wigner–Eckart Theorem; Fine and Hyperfine Structure of Energy Levels in Hydrogen-Like Atoms
- 18 Time-Dependent Perturbation Theory
- 19 Systems of Identical Particles
- Bibliography
- Index
15 - Scattering by a Potential
Published online by Cambridge University Press: 05 December 2024
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- 1 The Failure of Classical Physics
- 2 Wave–Particle Duality andWave Mechanics
- 3 Schrödinger Equation; Uncertainty Relations
- 4 The One-Dimensional Schrödinger Equation; Bound States
- 5 Scattering in One Dimension
- 6 Mathematical Formulation of Quantum Mechanics
- 7 Physical Interpretation: Postulates of Quantum Mechanics
- 8 The Harmonic Oscillator
- 9 Particle in a Central Potential; Orbital Angular Momentum
- 10 Bound States in a Central Potential: Applications
- 11 Angular Momentum: General Properties
- 12 Spin; Charged Particle in an Electromagnetic Field
- 13 Addition of Angular Momenta
- 14 Approximation Methods
- 15 Scattering by a Potential
- 16 Symmetry Transformations of States and Operators
- 17 Rotation Matrices and the Wigner–Eckart Theorem; Fine and Hyperfine Structure of Energy Levels in Hydrogen-Like Atoms
- 18 Time-Dependent Perturbation Theory
- 19 Systems of Identical Particles
- Bibliography
- Index
Summary
Derivation of the Born approximation and criteria for its validity; applications of the Born approximation to scattering in Coulomb and Yukawa potentials; derivation of the optical theorem; perturbative expansion of the scattering wave function and scattering amplitude; scattering in a hard-sphere potential at low and high energy; scattering in potential well and resonances; partial wave expansion of the integral equation for scattering in a central potential; scattering in a spin-dependent potential; phase shifts in Born approximation; effective range theory; phase shifts at high energy and the eikonal approximation for the scattering amplitude.
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- Information
- Quantum Mechanics through ProblemsWith Complete Solutions, pp. 516 - 581Publisher: Cambridge University PressPrint publication year: 2024