Humblet, J. (1985) Bessel function expansions of Coulomb wave functions. Journal of Mathematical Physics, 26 (4). pp. 656-659. ISSN 0022-2488 http://resolver.caltech.edu/CaltechAUTHORS:20120628-110022016
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From the convergence properties of the expansion of the function Φ_l∝r^(−l−1)F_l in powers of the energy, we successively obtain the expansions of F_l and G_l as single series of modified Bessel functions I_(2l+1+n) and K_(2l+1+n), respectively, as well as corresponding asymptotic approximations of G_l for ‖η‖→∞. Both repulsive and attractive fields are considered for real and complex energies as well. The expansion of F_l is not new, but its convergence is given a simpler and corrected proof. The simplest form of the asymptotic approximations obtained for G_l, in the case of a repulsive field and for low positive energies, is compared to an expansion obtained by Abramowitz.
|Additional Information:||© 1985 American Institute of Physics. Received 6 March 1984; accepted 12 October 1984. Most of this paper has been prepared at the W. K. Kellogg Radiation Laboratory of the California Institute of Technology. The author is very grateful to C. A. Barnes, W. A. Fowler, and S. E. Koonin for their warm hospitality during his stay at Caltech and their interest in this work.|
|Subject Keywords:||WAVE FUNCTIONS, BESSEL FUNCTIONS, SERIES EXPANSION, ASYMPTOTIC SOLUTIONS, POLYNOMIALS, DIFFERENTIAL EQUATIONS, GAMMA FUNCTION, RECURSION RELATIONS, POWER SERIES, BOUNDARY CONDITIONS, FIELD THEORIES, COULOMB SCATTERING, COULOMB FIELD|
|Classification Code:||PACS: 02.30.Gp, 02.30.Mv, 24.10.-i, 11.80.-m|
|Official Citation:||Bessel function expansions of Coulomb wave functions J. Humblet J. Math. Phys. 26, 656 (1985); http://dx.doi.org/10.1063/1.526602|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||28 Jun 2012 18:21|
|Last Modified:||26 Dec 2012 15:25|
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