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

Richard Durran, Andrew Neate, Aubrey Truman
2008 Journal of Mathematical Physics  
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
more » ... bit for eccentricities greater than 1/√(2) which do not occur classically.
doi:10.1063/1.2837434 fatcat:da6gbq734bcxvongrgjaaejt5y