Why Can Tight-Binding and DFT Models Assume Electrons are Non-Interacting?

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SUMMARY

Tight-binding and density functional theory (DFT) models assume electrons are non-interacting to simplify calculations and focus on electron density rather than individual interactions. These models effectively approximate the behavior of electrons in solids despite the presence of strong Coulombic interactions. The justification lies in the ability of these models to capture essential physical properties while minimizing computational complexity, making them valid for many practical applications in condensed matter physics.

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  • Understanding of tight-binding models in solid-state physics
  • Familiarity with density functional theory (DFT)
  • Knowledge of Coulombic interactions and their implications
  • Basic concepts of electron density and its significance in quantum mechanics
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  • Explore the mathematical foundations of tight-binding models
  • Study the principles of density functional theory (DFT) in detail
  • Investigate the role of Coulombic interactions in quantum systems
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Physicists, materials scientists, and researchers in condensed matter physics seeking to understand the simplifications in modeling electron interactions and the validity of theoretical frameworks like tight-binding and DFT.

Nusc
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What is the justification behind tight-binding, nearly free electron drude model, to assume electrons as non-interacting? Because it is clearly not the case when considering coloumbic interactions, why can these models do this? Coloumbic interactions are strong so I wouldn't consider them to be idealized.

Or why is density functional theory valid? How is it still valid by expressing things in terms of its electron density while neglecting couloumbic interactions?
 
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