Geodesic
Generalized coulomb Green's function for bound states of the nonrelativistic Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 7 (1971) no. 3, pp. 342-347

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The well-known closed expression for the Coulomb Green's function in the coordinate representation in terms of Whittaker functions is used to obtain an explicit expression for a generalized Coulomb Green's function for an arbitrary bound state of the nonretativistic Schrödinger equation in the three-dimensional case. Formulas are derived that express the corrections of the higher orders of perturbation theory in terms of the generalized Green's function. 
@article{TMF_1971_7_3_a5,
     author = {A. I. Sherstyuk},
     title = {Generalized coulomb {Green's} function for bound states of the nonrelativistic {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {342--347},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1971_7_3_a5/}
}
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A. I. Sherstyuk. Generalized coulomb Green's function for bound states of the nonrelativistic Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 7 (1971) no. 3, pp. 342-347. http://geodesic.mathdoc.fr/item/TMF_1971_7_3_a5/