The electron spin, which does not explicitly appear in the N-particle Hamiltonian of the solid (except for the spin-orbit coupling and Zeeman terms), will be in the focus of this chapter. Thus, the treatment of the homogeneous electron gas, the calculation of its ground state energy per particle (which in differentĪpproximations can be done even analytically) becomes an introduction to the concepts of many-body theory, which have theirīearings also in nuclear or astrophysics. The Coulomb interaction by a more general two-particle interaction – applies also to physical systems beyond solid state physics. This so-called jellium model (remember the difference between jelly and confiture) represents a many-body system of free charged fermions, which – replacing It is characterized by neglecting the structuralĪspects and by replacing the configuration of point-like positive ions by a homogeneous positive background charge to ensureĬharge neutrality of the system (Problem 4.1). In this chapter the much simpler problem of the homogeneous electron gas. Instead of this complex problem, for which only approximate solutions can be found with numerical methods, we want to consider
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