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In our previous discussions of the electronic structure of materials we have assumed the one-electron approximation. The energy levels and the band-structure were calculated for an electron in an effective potential consisting of the potential of the ion cores and an average potential due to the other electrons. Within this model quite acceptable bandstructures can be calculated. However, another aspect of the one-electron model is more important than the qualitative agreement with experiment and the (in principle) simple calculational method: Within the one-electron model it is also possible to understand conceptually the excited states of the electronic system, resulting for example from the interaction with photons and other particles or from thermal excitation. Just as the energy levels of the hydrogen atom serve as a model for describing the energy levels of all elements, so the one-electron model is the basic model for our understanding of the solid state. Furthermore, there are phenomena associated with the collective behavior of the electrons which can nonetheless be tackled within this framework; for example, Thomas-Fermi screening (Sect. 6.5) or the excitation of charge density waves (Sect. 11.9).
KeywordsExchange Interaction Curie Temperature Critical Exponent Spin Wave Exchange Coupling
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