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14.4: Optical Theorem

Last updated

Apr 1, 2025
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- 14.3: Partial Waves
- 14.5: Determination of Phase-Shifts

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A comparison between Equations ([e17.73]) and ([e17.75]) reveals that

$\sigma_{\rm total} = \frac{4\pi}{k}\,{\rm Im}[f(0)] = \frac{4\pi}{k}\, {\rm Im}(f({\bf k},{\bf k})],$ because

$P_l(0)=1$ . This result is known as the optical theorem , and is a consequence of the fact that the very existence of scattering requires scattering in the forward (

$\theta=0$ ) direction, in order to interfere with the incident wave, and thereby reduce the probability current in that direction.

Contributors and Attributions

Richard Fitzpatrick (Professor of Physics, The University of Texas at Austin)

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Contributors and Attributions

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