14.4: Optical Theorem

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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