On Green's functions, propagators, and sturmians for the nonrelativistic coulomb problem

Recent progress in the mathematical physics and quantum chemistry of Coulomb Green's functions is summarized. Analogy with the defining relation for the Green's function has led to a finite model for the Fermi contact interaction which avoids spurious divergences in second-order perturbation calculations. The Hamilton-Jacobi mechanics of the Coulomb problem is reviewed. A compact parametrization for Hamilton's principal and characteristic functions provides a key element in further developments. These include a semiclassical representation for the Coulomb propagator in Feynman's formalism and a new propagator in the domain of Coulomb Sturmian eigenstates. In projected applications, approximate many-electron Green's functions constructed from combinations of one-particle Coulomb propagators provide a basis for computation of atomic and molecular eigenvalue spectra.