This is a very general talk that uses background in quantum mechanics and semiclassical methods. I will try to explain the very deep connection between semiclassical approximations and DFT. My hope is to allow plasma physicists and other animals to see the relation between DFT and approximations they are more familiar with.
For the past 6 years, I and my group have been tackling this rather fundamental problem, finding many results, relevant to physics, chemistry, and applied mathematics. I will attempt to give some overview.