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

Durran, Richard; Neate, Andrew and Truman, Aubrey (2008). The divine clockwork: Bohr’s correspondence principle and Nelson’s stochastic mechanics for the atomic elliptic state. Journal of Mathematical Physics, 49(3), article no. 032102.

DOI: https://doi.org/10.1063/1.2837434

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 $\frac{1}{\sqrt2}$ which do not occur classically.

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About

  • Item ORO ID
  • 78998
  • Item Type
  • Journal Item
  • ISSN
  • 1089-7658
  • Project Funding Details
  • Funded Project NameProject IDFunding Body
    Not SetNot SetWelsh Institute for Mathematical and Computational Sciences (WIMCS)
  • Academic Unit or School
  • Faculty of Science, Technology, Engineering and Mathematics (STEM)
  • Copyright Holders
  • © 2008 American Institute of Physics
  • Depositing User
  • Andrew Neate
CORE (COnnecting REpositories)

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