The Kepler Problem (Part 5)

In Part 4 we saw how the classical Kepler problem is connected to a particle moving on the 3-sphere, and how this illuminates the secret symmetry of the Kepler problem. There are various ways to quantize the Kepler problem and obtain a description of the hydrogen atom’s bound states as wavefunctions on the 3-sphere. Here I’ll take a less systematic but quicker approach.

I’ll start with the space of wavefunctions on the 3-sphere, and describe operators on this space arising from rotational sy...