Hydrodynamic theory of density-response functions at a metal surface

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Abstract
The density response of a metal surface to charge and potential perturbations is derived using a hydrodynamic description of the mobile electrons. Spatial dispersion and Ohmic damping are allowed for and results are found for both the retarded and nonretarded cases. The theory is carried through via three separate schemes: the density response is found from second-quantized density operators, from the effect of an applied potential, and from the effect of applied charge and current sources. The formulas are compared to earlier work. We confirm the nonretarded results of Eguiluz, but not those of others.