##### Quantum Physics For Dummies Quantum physics experiments take place in the lab frame, but you do scattering calculations in the center-of-mass frame, so you have to know how to relate the angle between the two frames.

Here's how this works: The following figure shows scattering in the lab frame. Scattering in the lab frame.

One particle, traveling at is incident on another particle that's at rest and hits it. After the collision, the first particle is scattered at and the other particle is scattered at Now in the center-of-mass frame, the center of mass is stationary and the particles head toward each other. After they collide, they head away from each other at angles You have to move back and forth between these two frames — the lab frame and the center-of-mass frame — so you need to relate the velocities and angles (in a nonrelativistic way).

To relate the angles you start by noting that you can connect using the velocity of the center of mass, In addition, here's what you can say about the velocity of particle 1 after it collides with particle 2: Now you can find the components of these velocities: Dividing the equation in the second bullet by the one in the first gives you But wouldn't it be easier if you could relate by something that didn't involve the velocities, only the masses, such as the following?  And you can show that You can also use the conservation of momentum to say what happens after the collision. In fact, because the center of mass is stationary in the center-of-mass frame, the total momentum before and after the collision is zero in that frame, like this: Therefore And after the collision, which means that Also, if the collision is elastic, kinetic energy is conserved in addition to momentum, so that means the following is true: Substituting into this equation gives you Given these two equations, you can redo Dividing the magnitude of each side of by the magnitude of the above equation gives you And because you saw earlier that substituting into this equation gives you at last Okay, that relates which is what you were trying to do. Using the relation you can rewrite as the following: You can also relate You can show that which, using a little trig, means that You've now related the angles between the lab and center-of-mass frames.