The Dirac-Coulomb Sturmian functions in the Z=0 limit: properties and applications to series expansions of the Dirac Green function and the Dirac plane wave

摘要

Properties of the discrete Dirac-Coulomb Sturmian functions, invented recently by the author, have been investigated in the limit Z --> 0, where Z is a nuclear charge. Limiting forms of differential equations as well as orthogonality and closure relations obeyed by the Sturmians have been obtained. A Sturmian expansion of the radial Dirac Green function for E < mc(2) and two Sturmian expansions of the Dirac plane wave have been derived. [References: 15]