The Free Electron Gas
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Instead of this complex problem, for which only approximate solutions can be found with numerical methods, we want to consider in this chapter the much simpler problem of the homogeneous electron gas. It is characterized by neglecting the structural aspects and by replacing the configuration of point-like positive ions by a homogeneous positive background charge to ensure charge neutrality of the system (Problem 4.1). This so-called jellium model (remember the difference between jelly and confiture) represents a many-body system of free charged fermions, which – replacing the Coulomb interaction by a more general two-particle interaction – applies also to physical systems beyond solid state physics. Thus, the treatment of the homogeneous electron gas, the calculation of its ground state energy per particle (which in different approximations can be done even analytically) becomes an introduction to the concepts of many-body theory, which have their bearings also in nuclear or astrophysics.
KeywordsDielectric Function Ground State Energy Landau Level Jellium Model Fermi Sphere
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