Solid State Theory pp 75-115 | Cite as

# The Free Electron Gas

Chapter

## Abstract

The structure of a solid, its composition of atoms, as well as the electronic, optical and lattice properties are essentially determined by the electrons. However, not all electrons of the atoms constituting the solid are involved in the same way. At the beginning of Chap. 2 we have distinguished between the core electrons and the valence electrons. The former are tightly bound to the nuclei and extend over a distance (much) smaller than the lattice constant, while the wave functions of the latter overlap with those of the neighboring atoms, thus giving rise to the chemical binding. Therefore, we describe the solid as being composed out of ions (nuclei plus closed shell electrons) in equilibrium positions at .

**R**_{ n }^{0}and valence electrons, which are responsible for the stability of the solid and its electronic properties. They are ruled by the Hamiltonian$$
\mathcal{H} = \sum\limits_{l = 1}^N {\frac{{p_l^2}}{{2m}} + \frac{1}{2}\sum\limits_{\mathop {k,l{\text{ }} = {\text{ }}1}\limits_{k \ne l} }^N {\frac{{{e^2}}}{{4\pi {\varepsilon _0}\left| {{r_k} - {r_l}} \right|}}} } + \sum\limits_{n,l} {v({r_l} - R_n^0) + \sum\limits_{mn} {V(R_n^0 - R_m^0)} }
$$

(4.1)

## Keywords

Free Electron Dielectric Function Ground State Energy Landau Level Jellium Model
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## References

- 1.Arnold Sommerfeld 1868 – 1951Google Scholar
- 2.Lev Davidovich Landau 1908 – 1968, Nobel prize in physics 1962Google Scholar
- 3.Wolfgang Pauli 1900 – 1958, Nobel prize in physics 1945Google Scholar
- 4.Pieter Zeeman 1865 – 1943, Nobel prize in physics 1902Google Scholar
- 5.Sir Rudolf Ernst Peierls 1907 – 1995Google Scholar
- 6.Wander Johannes de Haas 1878–1960, P.M. van Alphen 1906–1967Google Scholar
- 7.Lev Vasiljevich Shubnikov 1901 – 1937Google Scholar
- 8.John Clarke Slater 1900 – 1976Google Scholar
- 9.Vladimir Fock 1898 – 1974Google Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 2004