PLASMONS IN 3, 2 AND ONE-DIMENSION

We present a unified derivation of the plasmon dispersion relation for three, two and one dimensional systems. We obtain exact results in the long-wavelength limit with the help of a hydrodynamic model. A heuristic description is also developed to help understanding the physics behind the plasmon in the three different dimensionalities and a quantum derivation is briefly presented in order to corroborate the hydrodynamic results.