Quantum Matter Lecture 16

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okay welcome back at the end of last lecture we were we just derived the so called NC density response function this is the response of arbitrary physical system to a potential perturbation at something wave vector K about potential couples to the density and then we make a measurement later of of the density and see how the system responds hence density density now um before going on we good what we going to do in this lecture we going to actually study this this expression and find out what its properties are for various different systems of fermions during the simple case of non interacting fermions and the more complicated case of interacting fermions but before doing so I want to just review how it is we we got here since it a fairly complicated formula so the way we did this is we started with some H Hamiltonian which is some H naught which is which are in general Hamiltonian it could have interactions in it or anything but we separate out from it the perturbation that we trying to measure the response to so there gonna be some Delta H and T which which is arbitrary