Electron transport in liquid metals I. The Boltzmann equation

It is shown how non-orthogonal sets of functions can be used to calculate the transport properties of electrons in a structurally disordered system of potential wells by means of a Boltzmann equation. The main modification introduced by using non-orthogonal functions as a representation is that the transition probability from a state s to a state sprime is given by 2π/h δ(Hss − Hsprime sprime) [H − Hss]ssprime [H − Hsprime sprime]sprime s where [H − Hss]ssprime is a matrix element of H − Hss and Hss is a diagonal matrix element of the Hamiltonian H. The construction of suitable representations for the cases of simple and noble liquid metals is described. The method provides a simple framework for developing a theory of liquid transition metals.