Abstract
The interaction of a point charge with surrounding media (the image potential) is analyzed using the quantum-mechanical description of dielectrics that consistently takes losses in media into account. We have derived a real dielectric function (without an imaginary part) appropriate for lossy dielectrics which, compared to the lossless one, significantly changes the image potential in the standard (first-order) calculations. However, when one adds to the Hamiltonian all higher-order terms caused by the losses, one finds that the image potential remains the same, as if there were no losses in media. Our calculations are approximative when analyzing complicated systems with various lossy dielectrics, but in some simple and essential cases (e.g., a dielectric plate) we are able to give the exact proof.
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