  We study the dynamic electronic polarizability of a single nano-scale
spherical metallic grain using quantum mechanical approach. We introduce the
model for interacting electrons bound in the grain allowing us numerically to
calculate the frequency dependence of the polarizability of grains of different
sizes. We show that within this model the main resonance peak corresponding to
the surface plasmon mode is blue-shifted and some minor secondary resonances
above and below the main peak exist. We study the behavior of blue shift as a
function of grain size and compare our findings with the classical
polarizability and with other results in the literature.
