The Drude formula of ac (frequency-dependent) electric conductivity has been established as a simple
and practically useful model to understand the electromagnetic response of simple free-electron-like
metals. In most textbooks of solid-state physics, the Drude formula is derived from either a
classical equation of motion or the semiclassical Boltzmann transport equation. On the other hand,
quantum-mechanical derivation of the Drude conductivity, which requires an appropriate treatment of
phonon-assisted intraband transitions with small momentum transfer, has not been well documented
except for the zero- or high-frequency case. Here, a lucid derivation of the Drude conductivity that
covers the entire frequency range is presented by means of quantum kinetic equations in the
density-matrix formalism. The derivation is straightforward so that advanced undergraduate students
or early-year graduate students will be able to gain insight into the link between the microscopic
Schrödinger…