  We analyze the electronic properties of a two-dimensional electron gas
rolled-up into a nanotube by both numerical and analytical techniques. The
nature and the energy dispersion of the electronic quantum states strongly
depend upon the geometric parameters of the nanotube: the typical radius of
curvature and the number of windings. The effect of the curvature results in
the appearance of atomic-like bound states localized near the points of maximum
curvature. For a two-dimensional sheet rolled up into an Archimedean spiral we
find that the number of bound states is equal to the number of windings of the
spiral.

Mesoscale and Nanoscale Physics