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

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.