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

Journal Article · Sat Mar 15 00:00:00 EDT 2008 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2837434· OSTI ID:21100226

Durran, Richard; Neate, Andrew; Truman, Aubrey ^[1]

---

1. Department of Mathematics, Swansea University, Singleton Park, Swansea, SA2 8PP, Wales (United Kingdom)

We consider the Bohr correspondence limit of the Schroedinger 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 (1/{radical}(2)) which do not occur classically.

• OSTI ID: 21100226
• Journal Information: Journal of Mathematical Physics, Vol. 49, Issue 3; Other Information: DOI: 10.1063/1.2837434; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
INSTABILITY
QUANTUM MECHANICS
SCHROEDINGER EQUATION
STOCHASTIC PROCESSES
WAVE FUNCTIONS