## Hartree-Fock by varying the coefficients of a wave function expansion

In our discussions hereafter we will use our definitions of single-particle states above and below the Fermi ($$F$$) level given by the labels $$ijkl\dots \le F$$ for so-called single-hole states and $$abcd\dots > F$$ for so-called particle states. For general single-particle states we employ the labels $$pqrs\dots$$.