The difference

[Maarten Carrette]

The first theorem states that for every unique external potential (crystal) there exist a unique density. This theorem doesn’t state anything about the shape, or anyother characteristic of that density.

The second theorom tells a little bit more about the properties of the density, more particularly that it reaches a global minimum for the energy, the energy of the system for the groundstate density. This can be used to find the groundstate density by minimizing the total energy functional.

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