Limiting behavior of quantum elastic collision

[jcap]

From the hyperphysics site http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2.html#c1 on classical elastic collisions I see that if an incoming particle of mass ##m_1## with velocity ##v_1## collides into a stationary target particle of mass ##m_2## then the velocity of the target particle after the collision, ##v_2'##, is given by:

$$v_2'=\frac{2m_1}{m_1+m_2}v_1.$$

Thus as the incoming particle mass ##m_1\rightarrow \infty## the velocity of the target particle ##v_2' \rightarrow 2 v_1##.

Does this behavior carry over to the case of quantum elastic collisions or does a very heavy incoming particle just fail to interact with a light target due to the large difference in masses?

 

[Nugatory]

Does this behavior carry over to the case of quantum elastic collisions

It carries over to the extent that the uncertainty principle allows. The relationship will hold for the expectation values of the velocities (although in practice it is usually easier to measure the momenta).

or does a very heavy incoming particle just fail to interact with a light target due to the large difference in masses?

That depends on the exact nature of the interaction, both classically and quantum mechanically. If the interaction doesn't produce an elastic collision then the formula doesn't apply.