Why Must Electron and Positron Have Equal Angles in Annihilation?

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SUMMARY

In the discussion regarding electron-positron annihilation, it is established that the angles of emission for both particles must be equal due to the principle of conservation of momentum. When an electron and positron collide, they possess equal mass, leading to the conclusion that their momentum vectors must balance out, resulting in equal angles, theta_1 and theta_2. This fundamental concept is crucial for understanding particle interactions in quantum theory.

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amy andrews
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Hi everyone,
I'm currently studying a bit of quantum theory and I came across this paragraph: When an electron collides with a positron, it moves with an angle theta_1 with the normal. Ditto for the positron, except that it has an angle theta_2. But the two angles must be equal. Why? Conservation of momentum.
Well, that was all the explanation given, and I don't understand the reasoning behind it, so could someone explain it to me? It would be very helpful during my self-study. (See the attached diagram)

Thank you!
 

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I can't formulate it for you mathematically, but since they have the same mass, wouldn't you EXPECT them to have the same angle?
 

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