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A new set of basis functions is introduced, consisting of products of Fermi-surface harmonics F₉ (k) and polynomials ₍ () in the energy (-) {k₁T}. The former are orthonormal on the Fermi surface, and the latter are orthonormal with weight function -. In terms of this set the exact semiclassical Boltzmann equation takes a particularly simple form, giving a matrix equation which can probably be truncated at low order to high accuracy. The connection with variational methods is simple. Truncating at a 1 1 matrix gives the usual variational solution where ₊ is assumed proportional to ₊ₗ for electrical conductivity and (-) ₊ₗ for thermal conductivity. Explicit equations are given for the matrix elements Q₉₍, ₉^{'n^'} of the scattering operator for the case of phonon scattering, and a perturbation formula for is given which is accurate for weak anisotropy. The matrix elements are simple integrals over spectral functions ^2 (, J, J^') F () which generalize the electron-phonon spectral function ^2F () used in superconductivity theory. Analogies are described between Boltzmann theory and Eliashberg theory for T₂ of superconductors. The intimate relations between high-temperature resistance and the s- or p-wave transition temperature are made explicit.
Philip B. Allen (Mon,) studied this question.