first Hohenberg-Kohn theorem

The main similarity I found is that both explanations say that the ground-state electron density determines the external potential. The video develops the idea in more detail using the relations between the external potential, the ground-state wave function and the electron density. It discusses whether these relations are one-to-one, showing why we can also go from the density back to the external potential. For me, the video focuses more on why this relation exists, while Wikipedia focuses more directly on the result of the theorem.