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How to Find the Resulting Angles in a Lab-Frame Collision between Particles of Equal Mass

Say you have two particles of equal mass colliding in a lab frame (where one particle starts at rest). You want to show that the two particles end up traveling at right angles with respect to each other in the lab frame. Using quantum physics, you can.

Note that if m1 = m2, then

image0.png

Note also that

image1.png

You know that

image2.png

tells you that the following is true:

image3.png

So substituting

image4.png

into the preceding equation gives you

image5.png

Therefore,

image6.png

the angles of the particles in the lab frame after the collision, add up to

image7.png

are at right angles with respect to each other. Cool.

In this case, you can use the relations you’ve already derived to get these relations in the special case where m1 = m2:

image8.png
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