Density functional theory is a very active field of research, and is of great importance in today’s science. It is founded by the Hohenberg-Kohn theorem, a strinking result stating that all the information of a quantum mechanical system is contained in its ground-state one-body density only. In 1983, Lieb remarked that the rigorous proof relies on a unique continuation property for many-body (magnetic) Schrödinger operators. We will introduce the Hohenberg-Kohn theorem, show why it reduces to a strong unique continuation problem, and explain how our Carleman estimate involving fractional Laplacians solves it. Based on https://arxiv.org/abs/1901.03207