The Divine Clockwork: Bohr's correspondence principle and Nelson's stochastic mechanics for the atomic elliptic state

TL;DR

This paper connects quantum wave functions of atomic states with classical Keplerian orbits using Nelson's stochastic mechanics, demonstrating how quantum limits can reproduce planetary motion laws.

Contribution

It introduces a novel approach linking quantum atomic states to classical Keplerian orbits through stochastic mechanics, solving a long-standing problem.

Findings

Trajectories converge to Keplerian motion in the quantum limit

Local instabilities occur for high eccentricities in the quantum setting

Provides a quantum mechanical derivation of Kepler's laws

Abstract

We consider the Bohr correspondence limit of the Schrodinger wave function for an atomic elliptic state. We analyse this limit in the context of Nelson's stochastic mechanics, exposing an underlying deterministic dynamical system in which trajectories converge to Keplerian motion on an ellipse. This solves the long standing problem of obtaining Kepler's laws of planetary motion in a quantum mechanical setting. In this quantum mechanical setting, local mild instabilities occur in the Kelperian orbit for eccentricities greater than 1/\sqrt{2} which do not occur classically.