Drude-Lorentz free electron theory of electrical properties of metals, which used classical Boltzmann statistics, was updated by Sommerfield by using Fermi-Dirac statistics. But the assumptions of free electron theory were more or less all retained. This was a considerable improvement but was not enough. It predicts many quantities that were contradicted by experimental observations. Please note that up to this point no use of the lattice periodicity was made. There comes the quantum mechanics of electrons in periodic lattice (insulator or metal or semiconductor) and Bloch's theorem. The concepts of electron correlations and screening showed why the free electron theory was so successful after all and let to the way of Fermi liquid theory and quasiparticle concept which Landau introduced almost single handed. To understand and appreciate all these beautiful ideas and theory please read first the excellent text book of Ashcroft and Mermin especially chapters 1,2,3, 9, 13 and 17.
Drude-Lorentz free electron theory of electrical properties of metals, which used classical Boltzmann statistics, was updated by Sommerfield by using Fermi-Dirac statistics. But the assumptions of free electron theory were more or less all retained. This was a considerable improvement but was not enough. It predicts many quantities that were contradicted by experimental observations. Please note that up to this point no use of the lattice periodicity was made. There comes the quantum mechanics of electrons in periodic lattice (insulator or metal or semiconductor) and Bloch's theorem. The concepts of electron correlations and screening showed why the free electron theory was so successful after all and let to the way of Fermi liquid theory and quasiparticle concept which Landau introduced almost single handed. To understand and appreciate all these beautiful ideas and theory please read first the excellent text book of Ashcroft and Mermin especially chapters 1,2,3, 9, 13 and 17.
Please also read previous discussion in RG on free electron theory of Drude and Lorentz.
You can find information about the Sommerfeld and Quantum Mechanics theory for understanding electrical properties in "Condensed Matter Physics", M. P. Marder, 2000
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