Scattering 3d

Quantum Mechanics · Part 4

213 KB10 sections4 key equationsLaTeX typeset
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Table of Contents

  1. 1.Scattering Setup
  2. 2.Differential Cross Section
  3. 3.Total Cross Section
  4. 4.Partial Wave Expansion
  5. 5.Phase Shifts
  6. 6.Optical Theorem
  7. 7.Partial Wave Cross Sections
  8. 8.Low Energy (s-wave) Scattering
  9. 9.Resonance Scattering
  10. 10.Born Approximation

Key Equations

$$\psi(\vec{r}) \sim e^{ikz} + f(\theta,\phi)\frac{e^{ikr}}{r}$$
$$f(\theta) = \sum_{\ell=0}^\infty (2\ell+1)f_\ell P_\ell(\cos\theta)$$
$$\sigma_{\text{tot}} = \frac{4\pi}{k}\text{Im}[f(0)]$$
$$f \approx f_0 = -a_s$$

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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