Lectures in Scattering Theory

International Series of Monographs in Natural Philosophy

A. G. Sitenko, P. J. Shepherd

• Publisher: Pergamon
• Year: 2013
• Print ISBN:
  9780080165745
• eBook ISBN:
  9781483186825
• Topic: Physical Sciences
• Subtopic: Quantum Theory

Lectures in Scattering Theory discusses problems in quantum mechanics and the principles of the non-relativistic theory of potential scattering. This book describes in detail the properties of the scattering matrix and its connection with physically observable quantities. This text presents a stationary formulation of the scattering problem and the wave functions of a particle found in an external field. This book also examines the analytic properties of the scattering matrix, dispersion relations, complex angular moments, as well as the separable representation of the scattering amplitude. The text also explains the method of factorizing the potential and the two-particle scattering amplitude, based on the Hilbert-Schmidt theorem for symmetric integral equations. In investigating the problem of scattering in a three-particle system, this book notes that the inapplicability of the Lippman-Schwinger equations can be fixed by appropriately re-arranging the equations. Faddeev equations are the new equations formed after such re-arrangements. This book also cites, as an example, the scattering of a spin-1/2 particle by a spinless particle (such as the scattering of a nucleon by a spinless nucleus). This text is suitable for students and professors dealing with quantum mechanics, theoretical nuclear physics, or other fields of advanced physics.

Table of contents

• Front Cover
• Lectures in Scattering Theory
• Copyright Page
• Table of Contents
• Preface
• Chapter 1. Quantum-mechanical Description and Representations
• Chapter 2. The Scattering Matrix and Transition Probability
• 2.1. The Scattering Matrix
• 2.2. The Time-shift Operator in the Interaction Representation
• 2.3. Integrals of Motion and Diagonalization of the 5-Matrix
• 2.4. The Transition Probability per Unit Time
• 2.5. An Integral Equation for the /-Matrix
• 2.6. Transformation of the Scattering Matrix. Cross-sections
• Chapter 3. Stationary Scattering Theory
• Chapter 4. Wave Function of a Particle in an External Field
• Chapter 5. The Optical Theorem
• Chapter 6. Time Reversal and the Reciprocity Theorem
• Chapter 7. Analytic Properties of the Scattering Matrix
• Chapter 8. Dispersion Relations
• Chapter 9. Complex Angular Momenta
• Chapter 10. Separable Representation of the Scattering Amplitude
• Chapter 11. Scattering in a Three-particle System
• Chapter 12. Scattering of Particles with Spin
• Bibliography
• Index