A question about optical theorem

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    Optical Theorem
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Discussion Overview

The discussion revolves around the optical theorem in the context of scattering theory, particularly focusing on the implications of a perfectly reflective target (a mirror) in both classical and quantum mechanics. Participants explore the relationship between total cross section and scattering amplitude, as well as the phenomena of diffraction and tunneling.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions the validity of the optical theorem when considering a perfectly reflective mirror, noting that the scattering amplitude in the forward direction is zero while the total cross section remains nonzero due to reflection.
  • Another participant introduces the concept of the Arago spot in wave optics, suggesting that the forward scattering amplitude is never zero, even behind a metallic mirror.
  • A participant raises a question about the implications in quantum mechanics and whether a thicker metallic mirror results in a smaller total cross section due to weaker forward scattering.
  • One participant acknowledges the role of tunneling and diffraction in producing the Arago spot, indicating that these effects complicate the understanding of the optical theorem.
  • There is a discussion about the conditions under which diffraction may not occur, particularly when the diameter of the incident beam is small compared to the mirror, leading to speculation about the absence of the Arago spot in such cases.
  • Another participant suggests that the optical theorem applies to an incident plane wave and discusses the need to decompose a restricted beam into a plane wave basis.
  • One participant proposes that if the diameter of the mirror is sufficiently large, the incident flux can be treated as a plane wave, leading to a discussion about the implications for the optical theorem and the existence of transfer amplitude despite the scattering potential being infinite.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the optical theorem in the presence of a perfectly reflective mirror, with some arguing for the existence of the Arago spot and others questioning its applicability under certain conditions. The discussion remains unresolved with multiple competing perspectives on the topic.

Contextual Notes

Participants note limitations related to the assumptions about beam diameter, the nature of the incident wave, and the conditions under which diffraction occurs. The discussion highlights the complexity of applying the optical theorem in various scenarios without reaching a consensus.

ndung200790
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Optical theorem says that total cross section proportion to elastic scattering amplitude in the forward direction.Then if the target is absolutely reflective ''mirror''(in the case of quantum mechanics:scattering potential=infinity(r<a) and de Broglie wave leng limits to 0),in this case the scattering amplitude in forward direction is zero,but the total cross section is nonzero (because of reflection).So I do not understand the optical theorem.
 
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In wave optics the forward scattering amplitude is never zero. I.e. even behind some metallic mirror (in the distance of several hundred meters) a bright spot will appear in the shadow zone.
http://en.wikipedia.org/wiki/Arago_spot
 
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And what about in the case of quantum mechanics?And in optics the thicker metalic mirror the smaller the total cross section?Because the thicker mirror the weaker the forward scattering.
 
Now,I understand that it is not only because tunneling through barrier,but also because diffraction making the spot after mirror.
 
But in case incident flux having diameter of the beam is very small comparision with diameter of the ''mirror'' and in classical limit(de Broglie wave leng tends to zero) and the momentum of particle is absolutely defined.So I think that having only reflection,but not having diffraction,then in this case there were not Arago spot?
 
ndung200790 said:
But in case incident flux having diameter of the beam is very small comparision with diameter of the ''mirror''

I think the optical theorem refers to an incident plane wave. If the diameter of the incident beam is restricted, then you first have to decompose it in a plane wave basis.
 
In case the diameter of mirror large enough(the region of scattering potential),then we can consider the incident flux is plane wave despite of the diameter of incident beam is narrower than that of mirror(and in classical limit).In this case,with unitary property of S matrix we deduce the optical theorem.Then we are led to the transfer amplitude allways exists,despite of the scattering potential limits to infinity?
 

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