The sun runs on a reaction that is classically forbidden

Proton fusion in the sun requires quantum tunnelling. At solar-core temperatures the protons do not have the energy to cross their mutual electric repulsion.

Two protons must come within a fermi of each other to fuse, and their positive charges push. The thermal energy at 15 million kelvin is well below that barrier. Gamow showed that a quantum wave has a tail inside the forbidden region. The overlap is tiny. The sun has so many protons that tiny is enough.

The same tunnelling explains alpha decay of heavy nuclei, where a particle leaves a nucleus it was not allowed to leave. Stars are the slow version. Without it, hydrogen would sit unburned and there would be no daylight to read by.