Electrodynamics of a Semiclassical Free-Electron Gas

This article presents a simplified treatment of the high density, collisionless, free-electron gas, based on the ideas of a wave number and frequency-dependent conductivity and dielectric constant. The formalism is applied to solve a number of problems: the screening of the electrostatic potential of a foreign point charge placed in the electron gas, the rate of energy loss of a charged particle moving through the electron gas, plasma oscillations, the reflection of electromagnetic waves from the electron gas, and ultrasonic attenuation in metals due to the interaction of the sound waves with the conduction electrons. In a final section it is indicated how the methods may be generalized. Explicit expressions for the conductivity of the electron gas are obtained in an appendix.