Revisiting the Coulomb problem: A novel representation of the confluent hypergeometric function as an infinite sum of discrete Bessel functions

A. D. Alhaidari

Published 2021-12-14, updated 2022-07-24Version 2

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.