Introduction to Quantum Mechanics · Problem 10.19

Scattering — David J. Griffiths

Physics — Quantum Mechanics · optical-theorem

Problem

Prove the optical theorem, which relates the total cross-section to the imaginary part of the forward scattering amplitude:

\sigma = \frac{4\pi}{k}\,\text{Im}\left[f(0)\right]. \tag{10.104}

Hint: Use Equations 10.47 and 10.48.