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

2007/11/30 by Richard Durran, Andrew Neate, Aubrey Truman · 1 citation
Physics and Astronomy · #Bohr model #Classical limit #Context (archaeology) #Correspondence principle (sociology) #Elliptic function #Elliptic orbit #Limit (mathematics) #Motion (physics) #Quantum #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #Wave function #quant-ph #stochastic dynamics and bifurcation

paper · pdf · doi:10.1063/1.2837434

published as Journal of Mathematical Physics, 49, 032102 (2008) · 42 pages, 18 figures, with typos corrected, updated abstract and updated section 6.5

openalex publication_date 2008/03/01 · arxiv created 2008/05/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We consider the Bohr correspondence limit of the Schrödinger wave function for an atomic elliptic state. We analyze 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 Keplerian orbit for eccentricities greater than 12 which do not occur classically.

Citations

• Derivation of the Schrödinger Equation from Newtonian Mechanics
• �ber die Anwendung der Quantentheorie auf den Atombau
• Semiclassical Analysis of Low Lying Eigenvalues, II. Tunneling

Cited by

• On the divine clockwork: The spectral gap for the correspondence limit of the Nelson diffusion generator for the atomic elliptic state