The development of the quantum mechanical electron theory of metals: 1900-28

Abstract

The development of the electron theory of metals from Drude’s free electron picture to Bloch’s quantum mechanical treatment of electrons in crystal lattices reflects in structure the evolution of quantum mechanics itself. As in that development, the steps leading to the quantum theory of metals may be divided into three periods: classical, 1900-26; semi-classical, 1926-8; and modern, late 1928 onwards. The classical period was dominated by the model of Drude and Lorentz in which a metal contained an ideal gas of conduction electrons governed by kinetic theory. Although the failures and contradictions of the model were strikingly apparent by World War I, few useful new concepts were added until Pauli’s crucial application in 1926 of Fermi-Dirac statistics to metals opened up the semi-classical period. In the following two years Sommerfeld, and others in his circle, by further application of the new statistics within the framework of the classical Drude-Lorentz theory, were able to resolve most of that theory’s outstanding difficulties. But it was not until Bloch’s paper in August 1928 that the full machinery of quantum mechanics, developed in 1925-6, was brought to bear on solids, thereby spearheading the creation between 1928 and 1933, by the first generation of theoretical solid-state physicists including Peierls, Wilson, Mott and others, of the modern quantum theory of solids.