Home

Publications

Presentations

Tutorials

Images

Animations

Group Members

Diversions

Links


Institute of Optics

bar_yell

Quantum-classical correspondence in the hydrogen atom in weak external fields

Paolo Bellomo, C. R. Stroud, Jr., David Farrelly, and T. Uzer

Phys. Rev. A 58, 3896 (1998).


The complex processes leading to the collisional population of ultra-long-lived Rydberg states with very high angular momentum can be explained surprisingly well using classical mechanics. In this paper, we explain the reason behind this striking agreement between classical theory and experiment by showing that the classical and quantum dynamics of Rydberg electrons in weak, slowly varying external fields agree beyond the mandates of Ehrenfest's theorem. In particular, we show that the expectation values of angular momentum and Runge-Lenz vectors in hydrogenic eigenstates obey exactly the same perturbative equations of motion as the time averages of the corresponding classical variables. By time averaging the quantum dynamics over a Kepler period, we extend this special quantum-classical equivalence to Rydberg wave packets relatively well localized in energy. Finally, the perturbative equations hold well also for external fields beyond the Inglis-Teller limit, and in the case of elliptic states, which yield the appropriate quasiclassical initial conditions, the matching with classical mechanics is complete.


Click here to download the .pdf version of the paper bellomo982.pdf (319 KB)


Previous Abstract

Publications List

Next Abstract





Web page maintained by
Hideomi Nihira ( nihira@optics.rochester.edu ).
Last modified 13 September 2006