# Quantum Matter Lecture 12

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welcome back topic of today lecture is going to be we considering systems of interacting fermions before launching into hartree fock which is a pretty big subject let do a little bit of review of what we discussed last time about interacting interacting with fermions so we wrote a general Hamiltonian as a non interacting piece plus an interacting piece and this general Hamiltonian were going to work with it could work you know we could be applying it to electrons to neutrons in a neutron star to electrons in the atom it could be electrons to the metal it could be electrons in two dimensional electron gas could be helium three fermions in in a fluid really it really any fermionic system where we have just free fermions and a interaction between them a very very general problem that a lot of people have to worry about independent of your field the non interacting Hamiltonian we can write as very generally a single body part C the C dagger alpha C beta with some coefficient H alpha beta and it it so typical to to choose to work with the diagonal form sum over a absolutely not see that

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