Main theory to explain Type I superconductors very successfully.

TODO can someone please just give the final predictions of BCS, and how they compare to experiments, first of all? Then derive them.

High level concepts:

- the wave functions of pairs of electrons (fermions) get together to form bosons. This is a phase transition effect, thus the specific sudden transition temperature.
- the pairs form a Bose-Einstein condensate
- once this new state is reached, all pairs are somehow entangled into one big wave function, and you so individual lattice imperfections can't move just one single electron off trajectory and make it lose energy