S Matrix

Quantum Mechanics · Part 8

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Table of Contents

  1. 1.The S-Matrix Concept
  2. 2.Properties of S-Matrix
  3. 3.S-Matrix Elements
  4. 4.Relation to Scattering Amplitude
  5. 5.Partial Wave S-Matrix
  6. 6.Unitarity and Optical Theorem
  7. 7.Analytic Structure
  8. 8.Poles and Resonances
  9. 9.Multichannel Scattering
  10. 10.Elastic and Inelastic Cross Sections

Key Equations

$$|\psi_{out}\rangle = \hat{S}|\psi_{in}\rangle$$
$$f(\theta) = -\frac{m}{2\pi\hbar^2}T_{fi}$$
$$k = i\kappa, \quad E_b = -\frac{\hbar^2\kappa^2}{2m}$$
$$\sigma_{reac} = \frac{\pi}{k^2}\sum_\ell(2\ell+1)(1-|S_\ell|^2)$$

Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.

Course Context

This PDF is part of the Quantum Mechanics course on CoursesHub.World. Master quantum mechanics from mathematical foundations to advanced topics. Covers Hilbert spaces, wave functions, angular momentum, perturbation theory, scattering, and path integrals with 450+ pages ...

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