Abstract
We compare a variety of approximation schemes, all predicting the excitation structure of a semiconductor. All schemes are placed within one common framework, in which the electron self energy is the central quantity. In arriving at this self energy it turns out to be essential to screen the Coulomb interaction between electrons both statically and dynamically. We subsequently discuss the Hartree, Hartree-Fock, local density functional and Slater Xα schemes, which all lead to incorrect excitation structures, and the GW scheme of Hedin which, in view of recent successes, appears to be a very promising scheme.
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