1st vs 2nd Hohenberg-Kohn Theorem

[Leander Deleux]

I don’t agree. The 1st one tells you the density uniquely determines the external potential but that doesn’t automatically mean the ground-state energy can be obtained by a variational principle over densities. The 2nd theorem is needed to guarantee that the true ground-state density minimizes the energy functional, which is an extra step. So while they’re clearly connected, the 2nd adds a genuinely new statement about variational character.

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