I have recently started my phd on ab-initio simulations, and have several confusions about the calculations (lets say with a method like DFT) of solid crystal structures. 1. what exactly are the exchange and correlation phenomena. I have read texts and books which describe its physical effects (in the sense that ferromagnetism occurs due to exchange interaction). However my question actually is - is it some esoteric physics that we still do not know but have only yet observed or is it something which is included in the Hamiltonian of the Schroedinger equation but cannot be solved for exactly for many body problems ? 2. Same for spin-orbit coupling. though the physics of this is much more clear to me because I can see magnetic moments of moving charges interacting, again - are these not included in the Hamiltonian of the Schroedinger equation or is it that they cannot be solved for exactly. Once I have answers o these I would feel much easy to learn how to use DFT, etc. Since I do not want to have just an overview, please give me answers as detailed as you'd like.