How Is the Ion Lattice Approximation Justified in Electron Dynamics?

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Discussion Overview

The discussion centers on the justification of the ion lattice approximation in the context of electron dynamics, exploring its relationship to various approximations used in many-body electron problems, particularly in solid-state physics.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant notes that the ion lattice approximation involves treating N interacting electrons in a periodic lattice of positive ion cores and questions the justification for this approach.
  • Another participant introduces the "crude adiabatic approximation," suggesting that it assumes nuclei are at their equilibrium positions, and contrasts it with the more general "adiabatic approximation" which addresses the electronic problem based on the momentaneous position of the nuclei.
  • A participant queries whether the ion lattice approximation is related to the Born-Oppenheimer approximation.
  • In response, another participant affirms the connection and references a book discussing these concepts, indicating that it is a relevant source for further understanding.

Areas of Agreement / Disagreement

Participants appear to agree on the relationship between the ion lattice approximation and the adiabatic approximations, but the discussion does not reach a consensus on the justification of the ion lattice approximation itself.

Contextual Notes

The discussion does not resolve the specific conditions or limitations under which the ion lattice approximation is justified, nor does it clarify the implications of the various approximations mentioned.

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To solve the full many-body electron problem one often uses the approximation that the dynamics of the electron system, is that of N interacting electrons living in a periodic lattice of positive ion cores. What justifies this approximation and does it have a particular name?
 
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The approximation is here that the nuclei are assumed to be located at their equilibrium position. This is called the "crude adiabatic approximation". The "adiabatic approximation" (not the crude one) would solve the electronic problem for the momentaneous position of the nuclei.
 
okay is it related to the Born-Oppenheimer approximation?
 
Basically yes. This is discussed in the book by huang and born dynamical theory of crystal lattices which is also online
 

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