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A unified treatment of the non-relativistic and relativistic hydrogen atom II: the Green functions

R A Swainson, G W F Drake
1991 Journal of Physics A: Mathematical and General  
1991). A unified treatment of the non-relativistic and relativistic hydrogen atom II: The Green functions. Abstract. This is the second in a series of three papers in which it is shown how the radial pan of non-relativistic and relativistic hydrogenic bound-state calculations involving the Green functions can be presented in a unified manner. In this paper the non-relativistic Green function is examined in detail; new functional forms are presented and a clear mathematical progression is shown
more » ... ogression is shown to link these and most other known forms. A linear transformation of the four radial parts of the relativistic Green function is given which allows for the presentation o f this function as a simple generalization of the non-relativistic Green function. Thus, many properties of the non-relativistic Green function are shown to have simple relativistic generalizations. In particular, new recursion relations of the radial pans of both the non-relativistic and relativistic Green functions are presented, along with new expressions for the double Laplace transforms and recursion relations between the radial matrix elements. Anovel proof ofthe Sturmian form ofthe radial Green functions is given in an appendix.
doi:10.1088/0305-4470/24/1/020 fatcat:r2z54riprnelhfi3yte6zjj2tm