Issue
EPL
Volume 83, Number 1, July 2008
Article Number 10002
Number of page(s) 3
Section General
DOI http://dx.doi.org/10.1209/0295-5075/83/10002
Published online 11 June 2008
EPL, 83 (2008) 10002
DOI: 10.1209/0295-5075/83/10002

Uniform WKB approximation of Coulomb wave functions for arbitrary partial wave

N. Michel

Department of Physics, Graduate School of Science, Kyoto University - Kyoto 606-8502, Japan


received 26 February 2008; accepted in final form 14 May 2008; published July 2008
published online 11 June 2008

Abstract
Coulomb wave functions are difficult to compute numerically for extremely low energies, even with direct numerical integration. Hence, it is more convenient to use asymptotic formulas in this region. It is the object of this paper to derive analytical asymptotic formulas valid for arbitrary energies and partial waves. Moreover, it is possible to extend these formulas for complex values of the parameters.

PACS
02.30.Fn - Several complex variables and analytic spaces.
02.30.Gp - Special functions.

© EPLA 2008