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The Coulomb Green's function in IR 3 and its relation to the harmonic oscillator in IR 4
Author(s) -
Briels W. J.
Publication year - 1987
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560320305
Subject(s) - coulomb , harmonic oscillator , simple (philosophy) , transformation (genetics) , fourier transform , gaussian , function (biology) , coulomb wave function , space (punctuation) , gaussian function , harmonic , generating function , representation (politics) , relation (database) , simple harmonic motion , mathematical analysis , physics , quantum mechanics , mathematics , chemistry , computer science , philosophy , law , biology , operating system , biochemistry , epistemology , evolutionary biology , political science , electron , politics , gene , database
A very simple derivation of the Coulomb Green's function in IR 3 is presented, which is based on an application of the Kustaanheimo–Stiefel transformation directly to the equation defining the harmonic oscillator Green's function in IR 4 . The representation that we obtain makes it possible to Fourier transform the Green's function with respect to its space variables by means of a simple Gaussian integration. The method that we use can readily be applied to several other Hamiltonians.