The Coulomb Green's function in IR3 and its relation to the harmonic oscillator in IR4

W. J. Briels

doi:10.1002/qua.560320305

The Coulomb Green's function in IR³ and its relation to the harmonic oscillator in IR⁴

W. J. Briels^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

A very simple derivation of the Coulomb Green's function in IR³ 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 IR⁴. 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.

Original language	English
Pages (from-to)	349-359
Number of pages	11
Journal	International Journal of Quantum Chemistry
Volume	32
Issue number	3
DOIs	https://doi.org/10.1002/qua.560320305
Publication status	Published - Sep 1987

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abstract = "A very simple derivation of the Coulomb Green's function in IR3 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 IR4. 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.",

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AB - A very simple derivation of the Coulomb Green's function in IR3 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 IR4. 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.

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The Coulomb Green's function in IR³ and its relation to the harmonic oscillator in IR⁴

Abstract

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