Optical theorem | Wikipedia audio article
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Date: 30/12/2018

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SUMMARY
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In physics, the optical theorem is a general law of wave scattering theory, which relates the forward scattering amplitude to the total cross section of the scatterer.  It is usually written in the form

  
    
      
        
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    {\displaystyle \sigma _{\mathrm {tot} }={\frac {4\pi }{k}}~\mathrm {Im} \,f(0),}
  where f(0) is the scattering amplitude with an angle of zero, that is, the amplitude of the wave scattered to the center of a distant screen, and k is the wave vector in the incident direction.  
Because the optical theorem is derived using only conservation of energy, or in quantum mechanics from conservation of probability, the optical theorem is widely applicable and, in quantum mechanics, 
  
    
      
        
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    {\displaystyle \sigma _{\mathrm {tot} }}
   includes both elastic and inelastic scattering.  Note that the above form is for an incident plane wave; a more general form involving arbitrary outgoing directions k' invented by Werner Heisenberg can be written

  
    
      
        
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    {\displaystyle \mathrm {Im} ~f(\mathbf {\hat {k}} ',\mathbf {\hat {k}} )={\frac {k}{4\pi }}\int f(\mathbf {\hat {k}} ',\mathbf {\hat {k}} '')f(\mathbf {\hat {k}} '',\mathbf {\hat {k}} )~d\mathbf {\hat {k}} ''.}
  The optical theorem implies that an object that scatters any light at all (or electrons, neutrons, etc) will have a nonzero forward scattering amplitude f(0). However, the physically observed field in the forward direction is the sum of the (nonzero) scattered field and the incident field, which may add to zero.