Hohenberg-Kohn theorem

[Olivier N]

The video explains this idea using the mathematical concepts like injective and surjective functions, showing how the external potential, wave function, and density relate to one another. It emphasises that quantum mechanics can be approached using just the electron density, rather than the full wave function.

The Wikipedia article, meanwhile, provides a more formal and mathematical explanation. It not only describes the uniqueness of the external potential but also introduces the HK functional and explains that the Hamiltonian’s spectrum is a unique functional of the ground-state density.

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