How can momentum be conserved during particle desintegration?

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SUMMARY

The discussion centers on the conservation of momentum during the disintegration of a particle, represented by the equation 1 -> 2 + 3. The key conclusion is that the momentum relationship can be expressed as p1^2 = p2^2 + p3^2 + 2cos(theta)*p2*p3, where p1 is the momentum of the original particle, p2 and p3 are the momenta of the resulting particles, and theta is the angle between p2 and p3. The solution emphasizes using classical momentum conservation rather than 4-momentum, simplifying the approach to the problem.

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Homework Statement



Given the desintegration of one particle,

1 -> 2 + 3

then show that

p1^2 = p2^2+p3² + 2cos(theta)*p2*p3

p1: momentum particle to be desintegrated
p2, p3: momentum of the two resulting particles
theta: angle between 2 & 3


Homework Equations





The Attempt at a Solution



I tried using conservation of quadrivector
 
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I am curious as to why you attempted this via 4-momentum? Is the text you are working with promote that use?

Anyways, the way I would approach this is a lot simpler, you do not need 4-momentum. Think of this by looking at the conservation of momentum thus,

P1=P2+P3

and it follows that taking the inner product leads to

P1\cdotP1 = P12 = (P2+P3)\cdot(P2+P3).

Leaving the rest to you. Essentially this is the laws of cosines.
 

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