A Closed-Form Relation for Dimension-Dependent Two-Electron Matrix Elements of the Interelectronic Distance |
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Authors: | Shun S. Lo Daniel A. Morales |
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Affiliation: | (1) Departamento de Química, Facultad de Ciencias, Universidad de Los Andes, Mérida, 5101, Venezuela;(2) Facultad de Ciencias, Universidad de Los Andes, Apartado Postal A61, La Hechicera, Mérida, 5101, Venezuela |
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Abstract: | The evaluation of matrix elements of two electron atoms is fundamental for the study of the electronic properties of those systems. We add to this knowledge by presenting an explicit expression for the matrix elements of the inverse of the interelectronic distance of two-electron atoms in any spatial dimension D. The basis functions used are the D-dependent hydrogenic wavefunctions {1s2,2p2,3d2,4f2,5g2,...,21y2,...}, extending and including, in this way, the results of the previous basis set {1s2,2p2,3d2,4f2}. The methodology used does not employ Fourier integral transforms as in previous works but hypergeometric transformation formulas. |
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Keywords: | matrix elements high-dimensional systems two-electron atoms |
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