Anwser relation of theorem 1 and 2

[Wodan]

No, I wouldn’t say so. The first theorem proves that there is a one on one relation between V_(ext), the wavefunction and the density function, showing that the density function can be used in quantum mechanics as it contains the same information as the wavefunction. The second theorem talks about the behaviour of the functional of E_(V_ext)) and more specifically for what value density value the functional returns a minimal value. You could say that you need the first theorem to couple the energy functional and the density, but the two theorems really do describe separate things. The first theorem tells you nothing about the functional’s behaviour.

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