How Is the Ion Lattice Approximation Justified in Electron Dynamics?

In summary, the conversation discusses the use of approximations in solving the full many-body electron problem. One such approximation is the crude adiabatic approximation, in which the nuclei are assumed to be at their equilibrium position. This is related to the Born-Oppenheimer approximation and is discussed in the book "Dynamical Theory of Crystal Lattices" by Huang and Born.
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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.
 
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okay is it related to the Born-Oppenheimer approximation?
 
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Basically yes. This is discussed in the book by huang and born dynamical theory of crystal lattices which is also online
 

FAQ: How Is the Ion Lattice Approximation Justified in Electron Dynamics?

What is the ion lattice approximation?

The ion lattice approximation is a theoretical model used to describe the behavior of ions in a crystal lattice. It assumes that the ions are fixed in a regular lattice structure and interact with each other through electrostatic forces.

How does the ion lattice approximation differ from other models?

Unlike other models, the ion lattice approximation takes into account the specific arrangement of ions in a lattice, rather than treating them as a homogenous mass. This allows for a more accurate description of the properties and behavior of the crystal.

What are the limitations of the ion lattice approximation?

The ion lattice approximation is a simplified model and does not take into account factors such as thermal vibrations, defects in the lattice, and interactions with the surrounding environment. It also assumes that the ions are stationary, which may not always be the case.

What are some practical applications of the ion lattice approximation?

The ion lattice approximation is widely used in materials science and solid state physics to predict the properties of crystals, such as their thermal and electrical conductivity, and their response to external forces. It is also used in the development of new materials for various technological applications.

Can the ion lattice approximation be applied to all types of crystals?

No, the ion lattice approximation is most accurate for simple ionic crystals, where the ions are held together by strong electrostatic forces. It may not be as effective for more complex crystals with covalent or metallic bonding.

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