Equivalence of Born and eikonal identities

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SUMMARY

The discussion focuses on demonstrating the equivalence of the Born and eikonal identities at very high energies, specifically addressing two key points: (i) the identities become identical in the high-energy limit, and (ii) the eikonal amplitude adheres to the optical theorem. The participant suggests that transitioning from an exponential form to a trigonometric representation, as per Euler's theorem, may be necessary for the first point. They also express uncertainty regarding the optical theorem's application to the eikonal amplitude and seek accessible references for further understanding.

PREREQUISITES
  • Understanding of Born and eikonal scattering theories
  • Familiarity with high-energy physics concepts
  • Knowledge of Euler's theorem in mathematical physics
  • Basic grasp of optical theorems in quantum mechanics
NEXT STEPS
  • Study the derivation of the Born approximation in high-energy scattering
  • Research the eikonal approximation and its applications in particle physics
  • Explore the optical theorem and its implications in scattering theory
  • Review texts on advanced quantum mechanics that cover scattering amplitudes
USEFUL FOR

Postgraduate physics students, researchers in high-energy particle physics, and anyone seeking to deepen their understanding of scattering theories and their mathematical foundations.

GarethB
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I am required to show that
(i)in the upper limit of very high energies, the Born and eikonal identities are identical.
(ii)that the eikonal amplitude satisfies the optical theorem.

Regarding (i) I think it will involve changing from an exponential to a trig(Euler's theorem) but I could be wrong. The textbook says that sinχ=χ (I think that χ is the profile function).

Regarding (ii) I am clueless. I am trying to do postgrad physics after a period of 6 years since undergrad!
Please help!
 
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Ok I have just tried what I thought would be right and failed. Can anyone reference me to a text on this stuff that is understandable?
 

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