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Calculation of the exchange and the leading order correlation energy for the homogeneous electron gas in arbitrary dimension

Authors: Robert Schlesier

Ref.: Bachelor thesis, Martin-Luther University of Halle-Wittenberg (2020)

Abstract: The main aim of this thesis is to investigate the HEG in arbitrary dimensions. To do so this thesis first summarizes the main Ideas of Hartree-Fock and perturbation theory. Than it shows how one can use the corresponding tools to derive analytic expressions for the leading order contributions to the energy of the HEG in arbitrary dimensions. As it will turn one can expand the energy in terms of the Wigner-Seitz radius. Especially the algebraic structure of correlation energy will change for different dimensions. To obtain this result we will use the RPA.

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