Difference (Richard M. Martin)

[william]

The definition in the book “electornic structure” states:
Theorem I. For any system of interacting particles in an external potential V_ext(r),
the potential V_ext(r) is determined uniquely, except for a constant, by the ground-state
particle density n_0(r).

In this definition indeed they say there is a one to one correspondence, however, there is also a figure that consideres the Hohenberg Theorem as a circle where the external potential determines all states in the system, including the ground state and ground state density. Using the Hohenberg theorem, one can go from the density back to the external potential since it is uniquely determined, thus completing the circle.

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