Theory vs consequence

[Yannick]

If I understood KH1 correctly, an electron density n(r) of a system is equivalent to its many body wavefunction ,i.e, it determines all the observables of the system. The observables are then functionals of n(r). KH1 doesn’t provide an explicit prescription for those functionals O[n].

In case E_tot is the observable you are interested in ,KH2 provides explicitely a unique functional whose minimum corresponds to the ground state energy of a system.

[Yannick]

I am missing something in my understanding. I don’t quite see how the second image where you have an E_tot[n] that tells you there are electron densities n(r) that have lower energy then the ground state can be said to be a good functional. It predicts the wrong energy spectrum ? Someone could say its simply a wrong functional. It tells you for the supposed right n(r) that you derived from V_ext, the wrong total energy.

[Author]

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