The Kepler Problem (Part 10)

The poet Blake wrote that you can

see a world in a grain of sand.

Today we’ll see a universe in an atom!

We’ll see that states of the hydrogen atom correspond to states of a massless spin-½ particle in the Einstein universe—a closed, static universe where space is a 3-sphere.

The rotational symmetries of the Einstein universe correspond to symmetries of the hydrogen atom. The energy eigenstates of the massless spin-½ particle correspond in a one-to-one way to energy eigenstates of the hydrog...