Free Electron

Nusc

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?

Nusc

Nevermind I understand now.