On the frequencies of collective electron oscillations in nanotubes
A model for a nanotube and a simple approach to the problem of the collective electrons' oscillations as a whole in a nanotube are suggested. The frequencies of the oscillations of the electronic cloud as a whole along the axis of a nanotube, a, and perpendicular to it, t, are calculated as well as the frequency of the breathing mode, b. It is shown that a is inversely proportional to the square root of the length of a nanotube. The frequency t differs from the usual plasma frequency, p0, by a considerable numerical factor.