By Edwin Bidwell Wilson
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Additional info for A Statistical Discussion of Sets of Precise Astronomical Measurements IV
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9) i,j The term Ui,j describes the Coulomb repulsion Ui,j = e2 4π 0 | Ri − R j | (10) between two electrons on different sites (Ri = R j ). The on-site repulsion was chosen to Uii = 15eV. We solve the Hamiltonian H + HC within the Hartree approximation, wherein the many-body electron-electron interaction (9) is replaced by the electrostatic potential from charge distribution in the system. Hence, we replace (9) by the Hartree Hamiltonian HH = N ∑ Vi ni (11) i with Vi = N ∑ Ui,j j nj . (12) 40 Physics and Applications of Graphene - Theory The problem is solved self-consistently; after the initial determination of an eigensystem from Hamiltonian (6), the Coulomb part (11) is calculated and the eigensystem updated; this procedure is repeated until a converged solution is obtained.