Quantum Corrections in the Theory of the Anomalous Skin Effect

A comparison is made between the semiclassical and the quantum-mechanical treatment of the anomalous skin effect. The latter theory is based on the density matrix. The author calculates the value of the surface impedance with both theories. The difference depends on a parameter λ, which is the ratio of the skin depth to a typical de Broglie wavelength. This wavelength corresponds to the velocity component, normal to the surface, of an effective electron. The order of magnitude of the correction depends on the relaxation time, and can amount to 10% for sufficiently pure metals.