Density Functional Theory (DFT) is the main method used in practical computations to approximate solutions of the many-body Schrödinger equation. The main idea is to express everything in terms of the one-particle density instead of the many-body wave function. The Local Density Approximation (LDA) is the simplest nonlinear functional used in this context and it has played a central role in the construction of better empirical approximations since the 60s.

In this talk I will first explain what DFT and LDA are. I will then give the first rigorous justification of the LDA. More precisely, I will show that the exact Levy-Lieb functional of DFT converges to the LDA in the limit of very flat densities. Joint work with Elliott H. Lieb (Princeton) and Robert Seiringer (IST Austria).