Electrons in a Periodic Potential

  • Ulrich Rössler


In Chap. 4, the crystal structure of the solid has been suppressed by smearing out the periodic configuration of ions in the jellium model, because the many-body aspects of the electron–electron interaction stood 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 0 n,τ } of a crystal lattice. Therefore, we reverse the introduction of the jellium term in Sect. 4.3 with the replacement.

Note the simplified notation of the single-particle potential V (r l ), which does not explicitly refer to the ion positions. It is invariant under lattice translations and for all electrons. The Hamiltonian for a system of N electrons in the crystal volume with the Coulomb potential defines the starting point for this chapter.


Landau Level Periodic Potential Valence Band Maximum Conduction Band Minimum Reciprocal Lattice Vector 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Ulrich Rössler
    • 1
  1. 1.Inst. Theoretische PhysikUniversität RegensburgRegensburgGermany

Personalised recommendations