How Can We Derive the Wavelength Sum Formula in Electron/Positron Annihilation?

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Homework Help Overview

The discussion revolves around deriving a formula related to the wavelengths produced during electron-positron annihilation, specifically focusing on the relationship between the wavelengths of the resulting photons and the angle separating them. The subject area is primarily relativity.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to understand the relationship between the wavelengths of the photons produced in the annihilation process, with some suggesting the use of conservation laws. Questions about the definitions of terms and the setup of the problem are also raised.

Discussion Status

The discussion is ongoing with various approaches being suggested, including the use of conservation of energy and momentum. Some participants are questioning the clarity of the original poster's terminology and are encouraging the use of diagrams to aid understanding.

Contextual Notes

There is a mention of the complexity of the problem, indicating it may be at a college level, and the potential for messy algebra. Additionally, there is a suggestion that the original poster may not be familiar with certain concepts, such as 4-vectors.

Feynmanfan
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Well, I've been trying to figure out how to prove that when a positron and an electron annihilate and two photons are produced, the addition of their wavelengths equals

L1+L2=Lcompton(1-cos(theta)) where theta is the angle that separates both photons.

It's a relativity problem I guess. I keep trying E^2=Eo^2+c^2p^2 and other formulae but get no result.

Thanks for your help
 
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What is L?
 
I think he means lambda.
 
Who's wavelengths are u referring to...?Draw a diagram (not the Feynman diagram,it's useless) and use conservation of 4 momentum...

Daniel.
 
dextercioby said:
Draw a diagram (not the Feynman diagram,it's useless) and use conservation of 4 momentum...
Just in case the Original poster hasn't learned 4 vactor yet...

here is another way to approach this problem:
Use conservation of energy and momentum...
the algebra might be a little bit messy, this is college level problem, don't expect you can finish it in 10 minutes
 
He's Feynmanfan,he SHOULD know everything about Feynman diagrams & 4momentum conservation.

:wink:

Daniel.
 

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