The Solid as a Many-Particle Problem
As mentioned in Sect. 1.1, we understand the solid as being composed of ions (nuclei and closed electron shells) and valence electrons. A more rigorous approach would start from nuclei and electrons, but a simple consideration of the spatial extension of electrons in different shells of the isolated atoms shows immediately that this is not necessary. The wave functions of electrons in inner shells (the core electrons) with binding energies of hundreds or thousands of eV extend over a distance much smaller than the lattice spacing in a solid, as visualized in Fig. 2.1. In fact, when the atoms are assembled into the configuration of a crystal lattice (or likewise of a molecule, cluster, liquid) it will be the outermost, weakly bound valence electrons which first experience the presence of nearest neighbors. They will rearrange from their states in the isolated atoms into those which establish the chemical binding. Together with the electrostatic energy of the ion configuration, this defines the stable structure. Some textbooks on Solid State Theory start with a detailed description of this structure of crystalline solids (e.g. [4,7,9,11]) which is only briefly repeated here. Instead, we follow the approach of [5,14, 21] with a presentation of the basic Hamiltonian, which defines the solid as a quantum-mechanical many-body problem.
KeywordsCorrelation Function Response Function Dielectric Function Nobel Prize Kubo Formula
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- 1.Johannes Diderik van der Waals 1837 – 1923, Noble prize in physics 1910Google Scholar
- 2.Erwin Schrödinger 1887 – 1961, shared in 1933 the Nobel prize in physics with P.A.M. DiracGoogle Scholar
- 3.Max Born 1882 – 1970, Nobel prize in physics 1954; J. Robert Oppenheimer 1904 – 1967Google Scholar
- 4.Ludwig Boltzmann 1844 – 1906Google Scholar
- 5.Enrico Fermi 1901 – 1954, Nobel prize in physics 1938; Paul Adrien Maurice Dirac 1902 – 1984, Nobel prize in physics 1933Google Scholar
- 6.Satendra Nath Bose 1894 – 1974; Albert Einstein 1879 – 1955, Nobel prize in physics 1922Google Scholar
- 7.Alfred Lande 1888–1975Google Scholar
- 8.Niels Bohr 1885–1962, Nobel prize in physics 1922Google Scholar
- 9.Hendrik Anton Kramers 1894 – 1952; Ralph de Laer Kronig 1904 – 1995Google Scholar
- 10.George Green 1793–1841Google Scholar