Electrons in a Periodic Potential

  • Ulrich Rössler
Part of the Advanced Texts in Physics book series (ADTP)


In Chap. 4, where the crystal structure with the periodic configuration of ions has been smeared out by introducing the jellium model, the problem of electron-electron interaction was in the focus of interest. Now our attention will be in addition at the effect of the periodic potential formed by the ions in the configuration {R n, τ 0 } of a crystal lattice. This is done by reversing the introduction of the jellium term in Sect. 4.3
$$ {H_ + } \Rightarrow \sum\limits_{n,\tau ,l} {v\left( {{r_l} - R_{n,\tau }^0} \right) = \sum\limits_l {V\left( {{r_l}} \right)} } $$


Brillouin Zone Landau Level Periodic Potential Valence Band Maximum Conduction Band Minimum 
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  1. 1.
    Walther Kohn *1923, shared the Nobel prize in chemistry 1998 with J. PopleGoogle Scholar
  2. 2.
    Felix Bloch 1905 – 1983, Nobel prize in physics 1952Google Scholar
  3. 3.
    William B. Shockley 1910–1989, received the Noble prize in physics 1956 jointly with J. Bardeen and W.H. BrattainGoogle Scholar
  4. 4.
    Klaus von Klitzing *1943, Noble prize in physics 1985Google Scholar
  5. 5.
    Daniel C. Tsui *1939, Horst L. Stornier *1949, shared the Noble prize in physics 1998 with R.B. LaughlinGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Ulrich Rössler
    • 1
  1. 1.Institut für Theoretische PhysikUniversität RegensburgRegensburgGermany

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