Chapter 2: Many-body Schrödinger equation

In this chapter, we develop progressively better approximations to the many - body problem in terms of the independent electron approximation. In the notes, we will see that this results in novel terms to our potential that replace the two-body bare Coulomb potential. At the end, we show how the Hartree - Fock equations are obtained by imposing an antisymmetric ansatz for our wavefunctions, using the variational principle to minimize the energy with respect to variations in our single particle wavefunctions, and enforce the orthonormality constraint.