first Hohenberg Kohn theorem

[Martin Esteves]

Wikipedia explains the first H-K theorem as it follows: “The external potential (and hence the total energy), is a unique functional of the electron density.If two systems of electrons, one trapped in a potential v 1 and the other in v 2 , have the same ground-state density n then necessarily v 1 − v 2 = c o n s t”
Both (wikipedia, and the video) enphasises the idea of one invertible realtion between electorn density and external potential. However in the video it is explained its relationship with the wave function and the corollari wich express that anypropertie can be described as a functional of the electron desnity. So you could use it instead of the wave function to obtein all information of the sistem

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