Displacement Current in Classical and Quantum Systems

It is certain that electrical properties—whether slow (sec) or fast (nsec), even optical (fsec)—are described by Maxwell’s equations, and there are terms that depend on the rate of the change of the electric and magnetic fields. In particular, Maxwell’s equation for the curl of the magnetic field contains both the steady-state conduction current and a term depending upon the temporal derivative of the electric displacement field. The latter is referred to as the displacement current and is generally believed to have been included originally by Maxwell himself, although there is evidence it was earlier considered by Kirchhoff. Maxwell’s equations and Kirchoff’s circuit laws both are important over the wide range of frequencies with which electronics traditionally deal. Additionally, the displacement current is an important contribution to these in both classical and quantum mechanics. Here, the development of the displacement current, its importance in both classical and quantum mechanics, and some applications are provided to illustrate the fundamental role that it plays in the dynamics of a wide range of systems.