Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

Quantum-mechanical

In real metals, electrical screening is more complex than described above in the Fermi-Thomas theory. This is because Fermi-Thomas theory assumes that the mobile charges (electrons) can respond at any wave-vector. However, it is not energetically possible for an electron within or on a Fermi surface to respond at wave-vectors shorter than the Fermi wave-vector. This is related to the Gibbs phenomenon, where fourier series for functions that vary rapidly in space are not good approximations unless a very large number of terms in the series are retained. In physics this is known as Friedel oscillations, and applies both to surface and bulk screening. In each case the net electric field does not fall off exponentially in space, but rather as an inverse power law multiplied by an oscillatory term. The area of many-body physics devotes considerable effort to quantum-mechanical screening, which is very relevant to condensed matter physics.

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