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Blinder [Phys. Rev. A, 43, 13 (1991)] has given an explicit diagonal form for the nonrelativistic Coulomb propagator. His result is an infinite series involving Whittaker, Laguerre, Hermite, and error functions. However, he notes that at the nucleus, only error functions remain in the infinite series. Here, an off-diagonal generalization of Blinder's result at the nucleus is constructed. By relating this result to the Green function, it is then shown that one is led in this latter representation to an explicit sum of Blinder's infinite series. Finally, contact is established between the present off-diagonal study and the recent work of Chibisov et al. [Phys. Rev. Lett. 84, 451 (2000)] on the Coulomb Green function.

Off-diagonal properties of the Feynman propagator and the Green function for a bare Coulomb field