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Imagine dropping a ping pong ball of radius R onto an identical ping pong ball from a height of 10R. The balls undergo perfectly elastic collisions. What combination of delta x and delta p yield the most number of bounces while still satisfying the uncertainty relation delta x * delta p > hbar. Make any reasonable assumptions.

Now Classical physics allows perfect initial allignment and an infinite number of bounces if there are no pertubations. However there is a tradeoff in uncertainty of position (the farther away from center it hits the faster it will bounce off) and uncertainty in momentum (a bigger uncertainty there will lead to a "drift" of the ping pong ball away from the center, when we use quantum. How do we keep that durn ping pong ball on for as many bounces as physically possible.

I made some quick calculations and got about eight bounces