Relativistic wave and Green's functions for hydrogen--like ions

Abstract

The \textsc{Greens} library is presented which provides a set of C++ procedures for the computation of the (radial) Coulomb wave and Green's functions. Both, the nonrelativistic as well as relativistic representations of these functions are supported by the library. However, while the wave functions are implemented for all, the bound and free--electron states, the Green's functions are provided only for bound--state energies $(E < 0$). Apart from the Coulomb functions, moreover, the implementation of several special functions, such as the Kummer and Whittaker functions of the first and second kind, as well as a few utility procedures may help the user with the set--up and evaluation of matrix elements.