Ulam's Billiard: Classical vs. Quantum
In 1961, Stanislaw Ulam proposed a simple model: a particle bounces between a fixed wall and a wall that oscillates according to a piecewise-linear law. It seemed like just another billiard. But behind this simplicity lay a question that troubled physicists for decades: can the particle accelerate to infinity?
The answer turned out to be paradoxical. In the classical version, almost never.