Classical position probability densities for spherically symmetric potentials
Physics Education
2007-05-23 v1
Abstract
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and requires only elementary algebra and one tabulated integral. The method is applied to compute the distributions for the Kepler-Coulomb and isotropic harmonic oscillator potentials. Formulas are also deduced for the average values for powers of the radial coordinate, and applied to describe perturbations to these systems. The classical results are also compared with quantum mechanical calculations using the Einstein-Brillouin-Keller semiclassical quantization.
Cite
@article{arxiv.physics/0501111,
title = {Classical position probability densities for spherically symmetric potentials},
author = {Lorenzo J. Curtis and David G. Ellis},
journal= {arXiv preprint arXiv:physics/0501111},
year = {2007}
}
Comments
14 pages, 2 figures