Excited State Reduced Coulomb Green's Function and f-Dimensional Coulomb Green's Function in Momentum Space
- 1 November 1971
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 12 (11) , 2311-2319
- https://doi.org/10.1063/1.1665537
Abstract
An integral representation for the f‐dimensional nonrelativistic Coulomb Green's function in momentum space and an expansion of this function in a series of Gegenbauer polynomials are obtained. It is shown that the momentum space representatives of the f‐dimensional Coulomb Green's function and the related reduced Green's functions can be obtained by differentiation with respect to the momentum transfer of the corresponding functions in the one‐dimensional (f odd) or two‐dimensional (f even) case. Expressions in closed form are then obtained for the momentum space representatives in the one‐dimensional case of the full Coulomb Green's function and of the general nth excited state reduced Coulomb Green's function.Keywords
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