In lecture today, we were going through Griffith's QM, Chapter 7, The Variational Principle. The particular case is the ground state of Helium, where we consider the electron-electron interaction as a potential in the Hamiltonian. When all is said and done, we go further and kind of average out the effect of the screening by giving the atom an 'effective nuclear charge'. This seems a bit one-two-skip-a-fewish to me. Is their a solid theory behind this or does uncertainty restrict us from getting close enough to really model the situation. by the way, I've completely lost all understanding of an electron by now. I feel like these descriptions are all very statistical... is the electron really more like a gas distribution or is this just another case of sort of time-averaged statistical interpretation?