Abstract
The integral equation describing the dielectric response of a surface system cannot in general by solved analytically because quantum effects introduce a nonseparable kernel. An approximate separable kernel is proposed with which the static response problem (for the infinite surface barrier model) is readily solved in exact analytic form. The method, when tested for several physical problems, proves rather accurate and is then used to calculate the real self-energy of a test charge at arbitrary positions relative to the surface. Dynamical response are briefly discussed in the context of the dispersion of long-wave surface plasmons, for which an alternative iterative method is also proposed.
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