Arriving at Keplerian Orbits from the Quantum Elliptic State

My Quantum Physics III class involved studying and writing a paper about a selected topic in Quantum mechanics, and I studied the intersection of quantum and classical mechanics. A noisy classical system evolving via a classical path plus Brownian motion can be shown to follow quantum dynamics in the appropriate limit. This process can also be reversed, bringing a quantum system up to a noisy classical one. In my paper, I studied the typical two-body problem in the quantum regime and brought this up to the classical two-body problem. I showed that this process yields Kepler’s planetary laws, which, although not unexpected, is still quite neat!

As put in my conclusion: "However, supposing that Kepler was not interested in celestial mechanics, and no physicist after him had developed a solution to the two-body problem, we have shown that the motion of two classical bodies can be found starting from a quantum mechanical perspective."

The full paper can be read here for the intrepid quantum mechanist.