A systematic approach to the Hartree-Fock problem in the thermodynamic limit

A systematic procedure is proposed in order to look for non-plane-wave solutions to the Hartree-Fock equations in the thermodynamic limit. The corresponding Hartree-Fock states are seen to arise as the self-consistent eigenvectors of a special matrix, as in Roothaan's method. The attractive delta problem is tackled as an example. The corresponding solution fulfills the monotonicity requirement for the energy as a function of the density, which no other known solution to the problem verifies, and coincides, in the zero-density limit, with the lower bound of Lieb and de Llano.