A Neumann series of Bessel functions representation for solutions of the radial Dirac system

TL;DR

This paper introduces a novel Neumann series of Bessel functions representation for solutions of the radial Dirac system, enabling uniform convergence and facilitating numerical computation with practical examples.

Contribution

It provides a new analytical representation of the radial Dirac system solutions using Bessel functions, with formulas suitable for efficient numerical implementation.

Findings

Series converges uniformly with respect to the spectral parameter

Recurrent formulas enable efficient numerical computation

Numerical examples demonstrate the method's effectiveness

Abstract

A new representation for a regular solution of the radial Dirac system of a special form is obtained. The solution is represented as a Neumann series of Bessel functions uniformly convergent with respect to the spectral parameter. For the coefficients of the series convenient for numerical computation recurrent integration formulas are given. Numerical examples are presented.