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Analytically Reduced Form For The Class Of Integrals Containing Multicenter Products Of 1s Hydrogenic Orbitals, Coulomb Or Yukawa Potentials, And Plane Waves, Jack C. Straton
Physics Faculty Publications and Presentations
The class of integrals containing the product of N 1s hydrogenic orbitals and M Coulomb or Yukawa potentials with m plane waves is investigated analytically. The results obtained by Straton (1989) are extended and generalized. It is shown that the dimensionality of the entire class can be reduced from 3m to M+N-1.
Fourier Transform Of The Multicenter Product Of 1s Hydrogenic Orbitals And Coulomb Or Yukawa Potentials And The Analytically Reduced Form For Subsequent Integrals That Include Plane Waves, Jack C. Straton
Physics Faculty Publications and Presentations
The Fourier transform of the multicenter product of N 1s hydrogenic orbitals and M Coulomb or Yukawa potentials is given as an (M+N-1)-dimensional Feynman integral with external momenta and shifted coordinates. This is accomplished through the introduction of an integral transformation, in addition to the standard Feynman transformation for the denominators of the momentum representation of the terms in the product, which moves the resulting denominator into an exponential. This allows the angular dependence of the denominator to be combined with the angular dependence in the plane waves.