The science
The Sun's core is about 15 million kelvin. To fuse, two protons have to get close enough for the strong force to take over, but both are positively charged, and the electric repulsion between them (the Coulomb barrier, roughly 0.5–1 MeV high) is hundreds of times more than their typical thermal energy at the core (kT ≈ 1.3 keV). Climbing over it classically would take a temperature of around 10 billion kelvin.
Protons are also waves, and a wave doesn't stop dead at a barrier: a small part of it leaks through. George Gamow worked this out in 1928, and it's how stellar fusion rates are calculated.
The wave in this video is a real solution of the Schrödinger equation for a packet hitting a barrier.
Sources
- Standard solar model: central temperature about 15.7 million K (Bahcall et al.).
- Gamow (1928), Zeitschrift für Physik 51, 204: quantum tunnelling through a barrier.
