Revisiting the Coulomb problem: A novel representation of the confluent hypergeometric function as an infinite sum of discrete Bessel functions
Mathematical Physics
2023-03-23 v2 Functional Analysis
math.MP
Abstract
We use the tridiagonal representation approach to solve the radial Schr\"odinger equation for the continuum scattering states of the Coulomb problem in a complete basis set of discrete Bessel functions. Consequently, we obtain a new representation of the confluent hypergeometric function as an infinite sum of Bessel functions, which is numerically very stable and more rapidly convergent than another well-known formula.
Keywords
Cite
@article{arxiv.2112.07382,
title = {Revisiting the Coulomb problem: A novel representation of the confluent hypergeometric function as an infinite sum of discrete Bessel functions},
author = {A. D. Alhaidari},
journal= {arXiv preprint arXiv:2112.07382},
year = {2023}
}
Comments
7 pages, 1 table, 2 figures; improved version