Abstract
A useful representation for the radial part of the Coulomb Green's function is derived in the form of a double series in Laguerre polynomials with two free (arbitrary) parameters α and α′. An appropriate choice of α and α′ leads to a cardinal simplification in calculations of matrix elements involving Green's functions. The results are valid both in the nonrelativistic and in the relativistic case of the second-order Dirac equation. The momentum form of the nonrelativistic Green's function with free parameters is presented and a simple example of a two-photon extension of the well-known Gordon formula is given.
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